Exhibit 5.1

NORTH POINT • 901 LAKESIDE AVENUE • CLEVELAND, OHIO 44114.1190

TELEPHONE: +1.216.586.3939 • FACSIMILE: +1.216.579.0212

March 19, 2018

National Fuel Gas Company

6363 Main Street

Williamsville, New York 14221

Re: Registration Statement on Form S-3 Filed by National Fuel Gas Company

Ladies and Gentlemen:

We have acted as counsel for National Fuel Gas Company, a New Jersey corporation (the “Company”), in connection with the authorization of the possible issuance and sale from time to time, on a delayed basis, by the Company of an indeterminate amount of: (i) shares of common stock, par value $1.00 per share (the “Common Stock”), of the Company; (ii) debt securities of the Company (the “Debt Securities”); (iii) purchase contracts to purchase shares of Common Stock or other agreements or instruments requiring the Company to sell shares of Common Stock (the “Stock Purchase Contracts”); and (iv) units consisting of a Stock Purchase Contract and a beneficial interest in debt securities, trust preferred securities, preferred stock or debt obligations of either the Company or third parties, including U.S. Treasury securities, purchased with the proceeds from the sale of the units (“Stock Purchase Units”), in each case as contemplated by the Company’s Registration Statement on Form S-3 to which this opinion is an exhibit (as the same may be amended from time to time, the “Registration Statement”). The Debt Securities, Stock Purchase Contracts and Stock Purchase Units are collectively referred to herein as the “Securities” and each, a “Security.” The Securities may be offered and sold from time to time pursuant to Rule 415 under the Securities Act of 1933 (the “Securities Act”). The Debt Securities are to be issued under the Indenture, dated as of October 1, 1999 (as supplemented from time to time, the “Indenture”), between the Company and The Bank of New York Mellon (formerly known as The Bank of New York), as trustee (the “Trustee”).

In connection with the opinions expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinions. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that:

1. The Debt Securities, when duly executed by the Company and authenticated by the Trustee in accordance with the Indenture, issued and sold in accordance with the Registration Statement and delivered to the purchaser or purchasers thereof against receipt by the Company of such lawful consideration therefor as the Company’s Board of Directors (or a duly authorized committee or subcommittee thereof) may determine, will constitute valid and binding obligations of the Company.

ALKHOBAR • AMSTERDAM • ATLANTA • BEIJING • BOSTON • BRISBANE • BRUSSELS • CHICAGO • CLEVELAND • COLUMBUS • DALLAS • DETROIT • DUBAI • DÜSSELDORF • FRANKFURT • HONG KONG • HOUSTON • IRVINE • JEDDAH • LONDON • LOS ANGELES • MADRID MEXICO CITY • MIAMI • MILAN • MINNEAPOLIS • MOSCOW • MUNICH • NEW YORK • PARIS • PERTH • PITTSBURGH • RIYADH SAN DIEGO • SAN FRANCISCO • SÃO PAULO • SHANGHAI • SILICON VALLEY • SINGAPORE • SYDNEY • TAIPEI • TOKYO • WASHINGTON

National Fuel Gas Company

March 19, 2018

Page 2

2. The Stock Purchase Contracts, upon receipt by the Company of such lawful consideration therefor as the Company’s Board of Directors (or an authorized committee or subcommittee thereof) may determine, will constitute valid and binding obligations of the Company.

3. The Stock Purchase Units, upon receipt by the Company of such lawful consideration therefor as the Company’s Board of Directors (or an authorized committee or subcommittee thereof) may determine, will constitute valid and binding obligations of the Company.

In rendering the foregoing opinions, we have assumed that: (i) the Registration Statement, and any amendments thereto, will have become effective (and will remain effective at the time of issuance of any Securities thereunder); (ii) a prospectus supplement describing each class and/or series of Securities offered pursuant to the Registration Statement, to the extent required by applicable law and relevant rules and regulations of the Securities and Exchange Commission (the “Commission”), will be timely filed with the Commission; (iii) the definitive terms of each class and/or series of Securities will have been established in accordance with the authorizing resolutions adopted by the Company’s Board of Directors (or an authorized committee or subcommittee thereof) and, as applicable, the Company’s Restated Certificate of Incorporation, dated September 21, 1998 and Certificate of Amendment of Restated Certificate of Incorporation, dated March 14, 2005 (together, the “Certificate of Incorporation”), and applicable law; (iv) the Company will issue and deliver the Securities in the manner contemplated by the Registration Statement; (v) the resolutions authorizing the Company to issue, offer and sell the Securities will have been adopted by the Company’s Board of Directors (or an authorized committee or subcommittee thereof) and will be in full force and effect at all times at which the Securities are offered or sold by the Company; (vi) all Securities will be issued in compliance with applicable federal and state securities laws; and (vii) the Indenture and any Stock Purchase Contract Agreement or Stock Purchase Unit Agreement (each 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 any series of Debt Securities, we have further assumed that: (i) the Indenture is, and any supplemental indenture will be, a valid and binding obligation of the Trustee; (ii) all terms of such Debt Securities not provided for in the Indenture will have been established in accordance with the provisions of the Indenture and reflected in appropriate documentation approved by us and, if applicable, duly executed and delivered by the Company and the Trustee; and (iii) the Debt Securities will be executed, authenticated, issued and delivered in accordance with the provisions of the Indenture.

National Fuel Gas Company

March 19, 2018

Page 3

With respect to any Securities consisting of Stock Purchase Contracts, we have further assumed that: (i) the purchase contract agreement, approved by us, relating to the Stock Purchase Contracts (the “Stock 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 “Stock Purchase Contract Agent”) will have been authorized, executed and delivered by the Company and the Stock Purchase Contract Agent; and (ii) the Stock Purchase Contracts will be authorized, executed and delivered by the Company and the Stock Purchase Contract Agent in accordance with the provisions of the Stock Purchase Contract Agreement.

With respect to any Securities consisting of Stock Purchase Units, we have further assumed that: (i) the stock purchase unit agreement, approved by us, relating to the Stock Purchase Units (the “Stock Purchase Unit Agreement”) to be entered into between the Company and an entity selected by the Company to act as the purchase unit agent (the “Stock Purchase Unit Agent”) will have been authorized, executed and delivered by the Company and the Stock Purchase Unit Agent; (ii) the Stock Purchase Units will be authorized, executed and delivered by the Company and the Stock Purchase Unit Agent in accordance with the provisions of the Stock Purchase Unit Agreement; and (iii) each component of such Stock Purchase Unit will be authorized, validly issued, fully paid and nonassessable (to the extent applicable) and will constitute a valid and binding obligation of the Company or any third party (to the extent applicable) as contemplated by the Registration Statement and the applicable Stock Purchase Unit Agreement, if any.

For purposes of the opinions expressed herein, we have further assumed that: (i) the Company is, and will be at the time of issuance of any Securities, a corporation existing and in good standing under the laws of the State of New Jersey, (ii) the Securities, as applicable (A) will have been authorized by all necessary corporate action of the Company, (B) will have been executed and delivered by the Company under the laws of the State of New Jersey and (iii) the execution, delivery, performance and compliance with the terms and provisions of the Securities by the Company will not violate or conflict with the laws of the State of New Jersey, the terms and provisions of the Certificate of Incorporation of the Company, or any rule, regulation, order, decree, judgment, instrument or agreement binding upon or applicable to the Company under the State of New Jersey.

The opinions expressed herein are limited by bankruptcy, insolvency, reorganization, fraudulent transfer and fraudulent conveyance, voidable preference, moratorium or other similar laws and related regulations and judicial doctrines from time to time in effect relating to or affecting creditors’ rights generally, and by general equitable principles and public policy considerations, whether such principles and considerations are considered in a proceeding at law or at equity.

National Fuel Gas Company

March 19, 2018

Page 4

As to facts material to the opinions and assumptions expressed herein, we have relied upon oral or written statements and representations of officers and other representatives of the Company and others. The opinions expressed herein are limited to the laws of the State of New York, as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of the Registration Statement. In giving such consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day