Exhibit 5.1.1

NORTH POINT • 901 LAKESIDE AVENUE • CLEVELAND, OHIO 44114.1190

TELEPHONE: +1.216.586.3939 • FACSIMILE: +1.216.579.0212

September 27, 2017

National Fuel Gas Company

6363 Main Street

Williamsville, New York 14221

Re: $300,000,000 aggregate principal amount of 3.95% Notes due 2027

of National Fuel Gas Company

Ladies and Gentlemen:

We are acting as counsel for National Fuel Gas Company, a New Jersey corporation (the “Company”), in connection with the issuance and sale of $300,000,000 aggregate principal amount of the Company’s 3.95% Notes due 2027 (the “Notes”), pursuant to the Underwriting Agreement, dated as of September 18, 2017, entered into by and among the Company and Merrill Lynch, Pierce, Fenner & Smith Incorporated, U.S. Bancorp Investments, Inc. and Wells Fargo Securities, LLC, acting as representatives (in such capacity, the “Representatives”) of the several underwriters named therein. The Notes are being issued under the Indenture, dated as of October 1, 1999 (as supplemented, amended or otherwise modified to date, the “Indenture”), by and between the Company and The Bank of New York Mellon (formerly The Bank of New York), as trustee (the “Trustee”), including the terms of the Notes established as contemplated by Section 301 of the Indenture.

In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of this opinion.

Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that the Notes constitute valid and binding obligations of the Company.

The opinion set forth above is subject to the following limitations, qualifications and assumptions:

For purposes of the opinion expressed herein, we have assumed that (i) the Trustee has authorized, executed and delivered the Indenture, (ii) the Notes have been duly authenticated by the Trustee in accordance with the Indenture and (iii) the Indenture is the valid, binding and enforceable obligation of the Trustee.

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

September 27, 2017

Page 2

In rendering the foregoing opinion, we have further assumed that (a) the Company is a corporation existing and in good standing under the laws of the State of New Jersey, (b) the Indenture and the Notes have been (i) authorized by all necessary corporate action of the Company and (ii) executed and delivered by the Company under the laws of the State of New Jersey, and (c) the execution, delivery, performance and compliance with the terms and provisions of the Indenture and the Notes by the Company do not violate or conflict with the laws of the State of New Jersey or the terms and provisions of the Restated Certificate of Incorporation of the Company, as amended by the Certificate of Amendment of Restated Certificate Incorporation or the Bylaws of the Company, as amended, or any rule, regulation, order, decree, judgment, instrument or agreement binding upon or applicable to it or its properties.

The opinion expressed herein is limited by (i) 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 and remedies generally and (ii) general equitable principles and public policy considerations, whether such principles and considerations are considered in a proceeding at law or at equity.

As to facts material to the opinion and assumptions expressed herein, we have relied upon oral or written statements and representations of the officers and other representatives of the Company and others.

The opinion expressed herein is 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 Current Report on Form 8-K dated the date hereof filed by the Company and incorporated by reference into the Registration Statement on Form S-3 (Registration No. 333-202877) (the “Registration Statement”), filed by the Company to effect the registration of the Notes under the Securities Act of 1933 (the “Act”) and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of such 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 Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day