Exhibit 5.1

November 21, 2024

EOG Resources, Inc.

1111 Bagby, Sky Lobby 2

Houston, Texas 77002

Re: EOG Resources, Inc.

Registration Statement on Form S-3

File No. 333-261702

Ladies and Gentlemen:

We have acted as counsel to EOG Resources, Inc., a Delaware corporation (the “Company”), in connection with the registration, pursuant to (a) a Registration Statement on Form S-3 (File No. 333-261702) (the “Existing Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), and which became automatically effective on December 16, 2021, and (b) a prospectus supplement with respect thereto filed on November 18, 2024, with the Commission pursuant to Rule 424(b)(5) under the Act (the “Prospectus Supplement”) (pursuant to Rule 430B(f)(1) under the Act, information contained in the Prospectus Supplement that was omitted from the form of prospectus dated December 16, 2021 (the “Base Prospectus”) that is part of the Existing Registration Statement in reliance on Rule 430B(b) will be deemed part of and included in the Existing Registration Statement on the date specified in Rule 430B(f)(1) (the Existing Registration Statement, together with such information so deemed part thereof and included therein, the “Registration Statement”)), of the offering and sale by the Company of senior debt securities consisting of $1,000,000,000 aggregate principal amount of 5.650% Senior Notes due 2054 (the “Securities”) of the Company to be issued under an Indenture, dated as of May 18, 2009, between the Company and Computershare Trust Company, N.A. (as successor to Wells Fargo Bank, National Association), as trustee (in such capacity, the “Trustee”), as supplemented by an officers’ certificate delivered to the Trustee setting forth the specific terms applicable to the Securities (as so supplemented, the “Indenture”) and sold pursuant to the terms of an underwriting agreement, dated as of November 18, 2024, among the Company on the one hand, and J.P. Morgan Securities LLC, BofA Securities, Inc., Goldman Sachs & Co. LLC and Wells Fargo Securities, LLC, as representatives of the several underwriters named therein (together, the “Underwriters”), on the other hand (the “Underwriting Agreement” and, collectively with the Indenture, the “Transaction Documents”). This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Act.

We have examined originals or certified copies of such corporate records of the Company and other certificates and documents of officials of the Company, public officials and others as we have deemed appropriate for purposes of this letter. We have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to authentic original documents of all copies submitted to us as conformed, certified or reproduced copies, and that the Securities will conform to the specimen thereof we have reviewed. We have also assumed (i) the existence and entity power of each party to any document referred to herein other than the Company, and (ii) that the Indenture is a valid

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and binding obligation of the Trustee, enforceable against the Trustee in accordance with its terms. As to various questions of fact relevant to this letter, we have relied, without independent investigation, upon the recitals, certifications, statements, representations and warranties and agreements set forth in (i) the Transaction Documents and (ii) certificates of public officials and certificates of officers of the Company, all of which items specified in clauses (i) and (ii) we assume to be true, correct and complete.

Based upon the foregoing and subject to the assumptions, exceptions, qualifications and limitations set forth herein, we are of the opinion that when the Securities have been duly executed by the Company, duly authenticated by the Trustee in accordance with the terms of the Indenture, and delivered to and paid for by the Underwriters pursuant to the terms of the Underwriting Agreement, the Securities will be valid and binding obligations of the Company.

The opinions and other matters in this letter are qualified in their entirety and subject to the following:

A. We express no opinion as to the laws of any jurisdiction other than the laws of the State of Texas and the General Corporation Law of the State of Delaware.

B. The matters expressed in this letter are subject to and qualified and limited by (i) applicable bankruptcy, insolvency, fraudulent transfer and conveyance, reorganization, moratorium and similar laws affecting creditors’ rights and remedies generally, (ii) general principles of equity, including without limitation, concepts of materiality, reasonableness, good faith and fair dealing and the possible unavailability of specific performance or injunctive relief (regardless of whether considered in a proceeding in equity or at law), and (iii) securities laws and public policy underlying such laws with respect to rights to indemnification and contribution. We express no opinion as to the enforceability of Sections 113, 515 or 1301 of the Indenture.

C. This opinion letter is limited to the matters expressly stated herein and no opinion is to be inferred or implied beyond the opinion expressly set forth herein. We undertake no, and hereby disclaim any, obligation to make any inquiry after the date hereof or to advise you of any changes in any matter set forth herein, whether based on a change in the law, a change in any fact relating to the Company or any other person or any other circumstance.

We hereby consent to the filing of this opinion as an exhibit to a Current Report on Form 8-K filed by the Company with the Commission on or about the date hereof, to the incorporation by reference of this opinion into the Registration Statement and to the use of our name in the Base Prospectus and the Prospectus Supplement, forming a part of the Registration Statement under the caption “Legal Matters.” In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Act and the rules and regulations thereunder.

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Very truly yours,

/s/ Akin Gump Strauss Hauer & Feld LLP

AKIN GUMP STRAUSS HAUER & FELD LLP