Exhibit 5.1

February 26, 2024 Hess Corporation 1185 Avenue of the Americas New York, New York 10036 White & Case LLP 1221 Avenue of the Americas New York, NY 10020-1095 T +1 212 819 8200 whitecase.com

Ladies and Gentlemen:

We have acted as New York counsel to Hess Corporation, a corporation organized under the laws of Delaware (the “Company”), in connection with the preparation and filing by the Company with the Securities and Exchange Commission (the “Commission”) of an automatic shelf registration statement on Form S-3ASR (the “Registration Statement”) on the date hereof, relating to the registration under the Securities Act of 1933, as amended (the “Securities Act”), of the offer and sale by the Company of (i) shares of common stock of the Company, par value $1.00 per share (the “Common Stock”), (ii) shares of preferred stock of the Company, par value $1.00 per share (the “Preferred Stock”), which may be convertible into or exchangeable for Common Stock or certain other securities of the Company, (iii) debt securities consisting of debentures, notes or other evidences of indebtedness representing unsecured, unsubordinated obligations of the Company (the “Senior Debt Securities”), (iv) debt securities consisting of debentures, notes or other evidences of indebtedness representing unsecured, subordinated obligations of the Company (the “Subordinated Debt Securities” and together with the Senior Debt Securities, the “Debt Securities”), which may be convertible into or exchangeable for Common Stock or Preferred Stock of the Company, (v) warrants to purchase Debt Securities, Common Stock, Preferred Stock or Depositary Shares (as defined below) (the “Warrants”), (vi) depositary shares representing fractional or multiple interests in Preferred Shares (the “Depositary Shares”), (vii) contracts for the purchase or sale of Debt Securities, Preferred Stock, Common Stock, Depositary Shares or certain other securities of the Company (the “Purchase Contracts”) and (viii) units consisting of one or more Debt Securities, Warrants, Purchase Contracts, Preferred Stock or Depositary Shares (the “Units” and, collectively with the Common Stock, the Preferred Stock, the Debt Securities, the Warrants, the Depositary Shares and the Purchase Contracts, the “Securities”). The Securities that are being registered under the Registration Statement will have an indeterminate aggregate initial offering price and will be offered on a continuous or delayed basis pursuant to the provisions of Rule 415 under the Securities Act.

The Registration Statement includes a base prospectus relating to the offer and sale of the Securities (the “Base Prospectus”), which will be supplemented by one or more prospectus supplements in connection with the sale of the Securities. Each such prospectus supplement, together with the Base Prospectus, is referred to herein as a “Prospectus.”

This opinion letter is rendered in accordance with the requirements of Item 601(b)(5) of Regulation S–K under the Securities Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement, the Base Prospectus or any Prospectus filed pursuant to Rule 424(b) with respect thereto, other than as expressly stated herein with respect to the issue of the Securities.

In connection with our opinions expressed below, we have examined originals or copies certified or otherwise identified to our satisfaction of the following documents and such other documents, corporate records, certificates and other statements of government officials and corporate officers of the Company as we deemed necessary for the purposes of the opinions set forth in this opinion letter:

(a) the Registration Statement;

(b) the Base Prospectus;

(c) a copy of the Restated Certificate of Incorporation, as amended (the “Certificate of Incorporation”, dated May 3, 2006 filed as Exhibit 3.1 to the Company’s Quarterly Report on Form 10-Q for the three months ended June 30, 2006, as amended by the Amendments to the Certificate of Incorporation dated May 22, 2013 and May 12, 2014 filed as Exhibits 3.1 to the Company’s Current Reports on Form 8-K, filed with the Commission, respectively, on May 22, 2013 and May 13, 2014);

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(d) a copy of certificate of the Delaware Secretary of State, dated as of February 23, 2024, certifying the good standing of the Company under the laws of the State of Delaware;

(e) a copy of the By-laws of the Company, as amended effective May 6, 2020, filed as Exhibit 3.1 to the Company’s Quarterly Report on Form 10-Q for the three months ended March 31, 2020, as amended by the Amendment to the By-Laws dated October 22, 2023 filed as Exhibit 3.1 to the Company’s Form 8-K filed with the Commission on October 23, 2023;

(f) a copy of the resolutions adopted by the Company’s board of directors (the “Board”) on February 26, 2024; and

(g) the indentures pursuant to which the Senior Debt Securities and the Subordinated Debt Securities are to be issued (each, an “Indenture”), each dated as of March 1, 2006 between the Company and The Bank of New York Mellon, successor to JPMorgan Chase Bank, N.A., as trustee (the “Trustee”), filed as Exhibits 4 and 4.1, respectively, to the Registration Statement.

We have relied, to the extent we deem such reliance proper, upon such certificates or comparable documents of officers and representatives of the Company and of public officials and upon statements and information furnished by officers and representatives of the Company with respect to the accuracy of material factual matters contained therein which were not independently established by us. In rendering the opinions expressed below, we have assumed, without independent investigation or verification of any kind, the genuineness of all signatures on documents we have reviewed, the legal capacity and competency of all natural persons signing all such documents, the authenticity and completeness of all documents submitted to us as originals, the conformity to authentic, complete original documents of all documents submitted to us as copies, the truthfulness, completeness and correctness of all factual representations and statements contained in all documents we have reviewed, the accuracy and completeness of all public records examined by us, and the accuracy of all statements in certificates of officers of the Company that we reviewed.

In making our examination of documents executed by parties other than the Company, we have assumed (a) that such parties had the power, corporate or other, and authority to enter into and perform all their obligations thereunder, (b) the due authorization by all requisite action, corporate or other, and execution and delivery by such parties of such documents and the validity, binding and enforceable effect thereof in accordance with their respective terms and (c) that the Trustee is in compliance, generally and with respect to acting as trustee under the Indenture, with all applicable laws and regulations.

In rendering the opinions contained herein, we have assumed that: (i) the Registration Statement and any supplements and amendments thereto, will comply with all applicable laws (and will remain effective and in compliance at the time of issuance of any Securities thereunder); (ii) a prospectus supplement describing each class or series of Securities offered pursuant to the Registration Statement, to the extent required by applicable law and relevant rules and regulations of the Commission, will be timely filed with the Commission and will comply with all applicable laws; (iii) the definitive terms of each class or series of Securities will have been established in accordance with the authorizing resolutions adopted by the Board (or an authorized committee thereof), the Certificate of Incorporation and applicable law; (iv) the Company will issue and deliver the Securities in the manner contemplated by the Registration Statement including the Prospectus, and any Securities that consist of shares of capital stock will have been authorized and reserved for issuance, in each case within the limits of the then remaining authorized but unissued and unreserved amounts of such capital stock; (v) the resolutions authorizing the Company to issue, offer and sell the Securities will have been adopted by the Board (or an authorized committee thereof) and will be in full force and effect at all times when the Securities are offered or sold by the Company; (vi) all Securities will be issued and sold in compliance with applicable federal and state securities laws or applicable laws or regulations or any agreement or other instrument binding upon the Company; and (vii) any Indenture, form of note under such Indenture, form of Warrant, Warrant Agreement, Deposit Agreement, Purchase Contract Agreement or Unit Agreement (each as defined below) will be governed by and construed in accordance with the laws of the State of New York and will constitute a valid and binding obligation of each party thereto other than the Company.

With respect to any Securities consisting of Common Stock, we have further assumed that the Common Stock will be authorized, executed, countersigned by the transfer agent or registrar therefor and delivered by the Company in accordance with applicable laws and sold as contemplated in the Registration Statement.

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With respect to any Securities consisting of any series of Preferred Stock, we have further assumed that: (i) the certificate of designation, approved by appropriate corporate action, relating to the Preferred Stock establishing the designations, preferences and rights of the class or series of Preferred Stock (the “Certificate of Designation”), will have been authorized, executed and filed with the Secretary of State of the State of Delaware and (ii) the Preferred Stock will be authorized, executed, countersigned by the registrar and transfer agent therefor and delivered by the Company in accordance with the provisions of the Certificate of Designation and applicable laws and sold as contemplated in the Registration Statement.

With respect to any Securities consisting of any series of Debt Securities, we have further assumed that: (i) the applicable Indenture has been authorized, executed and delivered by the Company and the Trustee, (ii) the Debt Securities will be issued pursuant to the applicable Indenture, (iii) all terms of the Debt Securities not provided for in the applicable Indenture will have been established in accordance with the provisions thereof and reflected in appropriate documentation approved by appropriate corporate action and, if applicable, executed and delivered by the Company and authenticated by the Trustee, (iv) the Debt Securities will be authorized, executed, authenticated, issued and delivered by the Company and authenticated by the Trustee in accordance with the provisions of the applicable Indenture and applicable laws and sold as contemplated in the Registration Statement and (v) if the Debt Securities are convertible into Common Stock or Preferred Stock of the Company, (x) such Common Stock or Preferred Stock of the Company will be authorized by appropriate corporate action, (y) the Debt Securities will be presented for conversion in accordance with the terms thereof and (z) such Common Stock or Preferred Stock of the Company will be executed, countersigned by the transfer agent therefor and delivered by the Company upon such conversion, in accordance with the terms of such Debt Securities.

With respect to any Securities consisting of any series of Warrants, we have further assumed that: (i) the warrant agreement (if applicable), approved by appropriate corporate action, relating to the Warrants (the “Warrant Agreement”) to be entered into between the Company and an entity selected by the Company to act as the warrant agent (the “Warrant Agent”) will have been authorized, executed and delivered by the Company and the Warrant Agent and (ii) the Warrants will be authorized, executed, authenticated, issued and delivered by the Company and the Warrant Agent in accordance with the provisions of the form of Warrant, the Warrant Agreement (if applicable) and applicable laws and sold as contemplated in the Registration Statement.

With respect to any Securities consisting of Depositary Shares, we have further assumed that: (i) the deposit agreement, approved by appropriate corporate action, relating to the Depositary Shares (the “Deposit Agreement”) to be entered into between the Company and an entity selected by the Company to act as depository (the “Depositary”) will have been authorized, executed and delivered by the Company and the Depositary, (ii) the Company will deposit with the Depositary, Preferred Shares to be represented by the Depositary Shares that are authorized, validly issued and delivered as contemplated by the Registration Statement including the applicable Prospectus and the Deposit Agreement and (iii) the Depositary Shares will be authorized, executed, issued, fully-paid and delivered by the Company and the Depositary in accordance with the provisions of the Deposit Agreement and applicable laws and sold as contemplated in the Registration Statement.

With respect to any Securities consisting of Purchase Contracts, we have further assumed that: (i) the purchase contract agreement, approved by appropriate corporate action, relating to the Purchase Contracts (the “Purchase Contract Agreement”) to be entered into between the Company and an entity selected by the Company to act as the purchase contract agent (the “Purchase Contract Agent”) will have been authorized, executed and delivered by the Company and the Purchase Contract Agent and (ii) the Purchase Contracts will be authorized, executed, authenticated, issued and delivered by the Company and the Purchase Contract Agent in accordance with the provisions of the Purchase Contract Agreement and applicable law and sold as contemplated in the Registration Statement.

With respect to any Securities consisting of Units, we have further assumed that: (i) the unit agreement, approved by appropriate corporate action, relating to the Units (the “Unit Agreement”) to be entered into between the Company and an entity selected by the Company to act as the unit agent (the “Unit Agent”) will have been authorized, executed and delivered by the Company and the Unit Agent and (ii) the Units and each component of the Units will be authorized, executed, authenticated, issued, fully paid and non-assessable (to the extent applicable) and delivered by the Company and the Unit Agent in accordance with the provisions of the Unit Agreement and applicable laws and

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sold as contemplated in the Registration Statement and each component of the Units will constitute a valid and binding obligation of the Company or any third party (to the extent applicable) as contemplated by the Registration Statement including the Prospectus and the Unit Agreement.

With respect to any Securities issuable upon exercise, exchange or conversion of other Securities, in addition to the above assumptions as applicable, we have further assumed that such Securities issuable upon such exercise, exchange or conversion will be presented for exercise, exchange or conversion in accordance with the terms thereof and authorized, executed, countersigned by the transfer agent or registrar therefor and delivered by the Company upon such exercise, exchange or conversion in accordance with the terms thereof.

Based upon the foregoing assumptions and the assumptions set forth below, and subject to the qualifications and limitations stated herein, having considered such questions of law as we have deemed necessary as a basis for the opinions expressed below, we are of the opinion that:

1. The Common Stock (including Common Stock issuable upon exercise, exchange or conversion of other Securities), upon receipt by the Company of such lawful consideration therefor as the Board (or an authorized committee thereof) may determine, will be validly issued, fully paid and non-assessable shares of common stock, par value $1.00 per share, of the Company.

2. The Preferred Stock (including Preferred Stock issuable upon exercise, exchange or conversion of other Securities), upon receipt by the Company of such lawful consideration therefor as the Board (or an authorized committee thereof) may determine, will be validly issued, fully paid and non-assessable shares of preferred stock, par value $1.00 per share, of the Company.

3. The Debt Securities (including Debt Securities issuable upon exercise, exchange or conversion of other Securities), upon receipt by the Company of such lawful consideration therefor as the Board (or an authorized committee thereof) may determine, will constitute valid and binding obligations of the Company under the laws of the State of New York, enforceable against the Company in accordance with their terms, subject to (i) bankruptcy, insolvency, receivership, conservatorship, liquidation, reorganization, fraudulent transfer, moratorium or other laws affecting the enforcement of creditors’ rights generally, and by the application of general principles of equity (whether applied by a court in equity or at law) and the discretion of the court before which any proceedings therefor may be brought (such principles of equity are of general application, and in applying such principles, a court may include a covenant of good faith and fair dealing and apply concepts of reasonableness, mutuality and materiality); (ii) requirements that a judgment for money damages rendered by a court in the United States be expressed only in U.S. dollars; and (iii) governmental authority to limit, delay, or prohibit the making of payments outside the United States or in foreign currency or composite currency. Rights to indemnification and contribution may also be limited by Federal and state securities laws.

4. The Warrants, upon receipt by the Company of such lawful consideration therefor as the Board (or an authorized committee thereof) may determine, will constitute valid and binding obligations of the Company under the laws of the State of New York, enforceable against the Company in accordance with their terms, subject to (i) bankruptcy, insolvency, receivership, conservatorship, liquidation, reorganization, fraudulent transfer, moratorium or other laws affecting the enforcement of creditors’ rights generally, and by the application of general principles of equity (whether applied by a court in equity or at law) and the discretion of the court before which any proceedings therefor may be brought (such principles of equity are of general application, and in applying such principles, a court may include a covenant of good faith and fair dealing and apply concepts of reasonableness, mutuality and materiality); (ii) requirements that a judgment for money damages rendered by a court in the United States be expressed only in U.S. dollars; and (iii) governmental authority to limit, delay, or prohibit the making of payments outside the United States or in foreign currency or composite currency. Rights to indemnification and contribution may also be limited by Federal and state securities laws.

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5. The Depositary Shares, upon receipt by the Company of such lawful consideration therefor as the Board (or an authorized committee thereof) may determine, will be validly issued and the depositary receipts representing the Depositary Shares will entitle the holders thereof to the rights specified therein and in the Deposit Agreement pursuant to which they are issued, subject to (i) bankruptcy, insolvency, receivership, conservatorship, liquidation, reorganization, fraudulent transfer, moratorium or other laws affecting the enforcement of creditors’ rights generally, and by application of general principles of equity (whether applied by a court in equity or at law) and the discretion of the court before which any proceedings therefor may be brought (such principles of equity are of general application, and in applying such principles, a court may include a covenant of good faith and fair dealing and apply concepts of reasonableness, mutuality and materiality); (ii) requirements that a judgment for money damages rendered by a court in the United States be expressed only in U.S. dollars; and (iii) governmental authority to limit, delay, or prohibit the making of payments outside the United States or in foreign currency or composite currency. Rights to indemnification and contribution may also be limited by Federal and state securities laws.

6. The Purchase Contracts, upon receipt by the Company of such lawful consideration therefor as the Board (or an authorized committee thereof) may determine, will constitute valid and binding obligations of the Company under the laws of the State of New York, enforceable against the Company in accordance with their terms, subject to (i) bankruptcy, insolvency, receivership, conservatorship, liquidation, reorganization, fraudulent transfer, moratorium or other laws affecting the enforcement of creditors’ rights generally, and by the application of general principles of equity (whether applied by a court in equity or at law) and the discretion of the court before which any proceedings therefor may be brought (such principles of equity are of general application, and in applying such principles, a court may include a covenant of good faith and fair dealing and apply concepts of reasonableness, mutuality and materiality); (ii) requirements that a judgment for money damages rendered by a court in the United States be expressed only in U.S. dollars; and (iii) governmental authority to limit, delay, or prohibit the making of payments outside the United States or in foreign currency or composite currency. Rights to indemnification and contribution may also be limited by Federal and state securities laws.

7. The Units, upon receipt by the Company of such lawful consideration thereof as the Board (or an authorized committee thereof) may determine, will constitute valid and binding obligations of the Company under the laws of the State of New York, enforceable against the Company in accordance with their terms, subject to (i) bankruptcy, insolvency, receivership, conservatorship, liquidation, reorganization, fraudulent transfer, moratorium or other laws affecting the enforcement of creditors’ rights generally, and by the application of general principles of equity (whether applied by a court of law in equity or at law) and the discretion of the court before which any proceedings therefor may be brought (such principles of equity are of general application, and in applying such principles, a court may include a covenant of good faith and fair dealing and apply concepts of reasonableness, mutuality and materiality); (ii) requirements that a judgment for money damages rendered by a court in the United States be expressed only in U.S. dollars; and (iii) governmental authority to limit, delay, or prohibit the making of payments outside the United States or in foreign currency or composite currency. Rights to indemnification and contribution may also be limited by Federal and state securities laws.

The opinions expressed above are limited to questions arising under the law of the State of New York and the Delaware General Corporation Law. We do not express any opinion as to the laws of any other jurisdiction.

This opinion letter is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Securities Act.

The opinions expressed above are as of the date hereof only, and we express no opinion as to, and assume no responsibility for, the effect of any fact or circumstance occurring, or of which we learn, subsequent to the date of this opinion letter, including, without limitation, legislative and other changes in the law or changes in circumstances affecting any party. We assume no responsibility to update this opinion letter for, or to advise you of, any such facts or circumstances of which we become aware, regardless of whether or not they affect the opinions expressed in this opinion letter.

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We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement and to the reference to our firm as counsel for the Company that has passed on the validity of the Securities appearing under the caption “Validity of the Securities” in the Base Prospectus forming part of the Registration Statement or any Prospectus. In giving this consent, we do not hereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission thereunder.

The opinions expressed above are limited to the matters stated in this opinion letter, and no opinion is implied or may be inferred beyond those expressly stated in this opinion letter.

Very truly yours,

/s/ White & Case LLP

DJ/EG/MA/BM/RO

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