Exhibit 5.1

[Letterhead of White & Case LLP]

June 24, 2014

Hess Corporation

1185 Avenue of the Americas

New York, New York 10036

Ladies and Gentlemen:

We have acted as counsel for Hess Corporation, a Delaware corporation (the “Company”), in connection with the issuance of $300,000,000 aggregate principal amount of the Company’s 1.30% Notes due 2017 and $300,000,000 aggregate principal amount of the Company’s 3.50% Notes due 2024 (the “Notes”), under an Indenture, dated as of March 1, 2006 (the “Indenture”), between the Company and The Bank of New York Mellon, as successor-in-interest to JPMorgan Chase Bank N.A., as trustee (the “Trustee”) and pursuant to a Registration Statement on Form S-3 (File No. 333-179744) (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Act”) filed with the Securities and Exchange Commission (the “Commission”) on February 27, 2012, a Prospectus, dated February 27, 2012, forming part of the Registration Statement (the “Base Prospectus”), a Prospectus Supplement, dated June 19, 2014, relating to the Notes, filed with the Commission pursuant to Rule 424(b) under the Act (the “Prospectus Supplement” and together with the Base Prospectus, the “Prospectus”) and an Underwriting Agreement dated June 19, 2014 (the “Underwriting Agreement”) among the Company, on the one hand, and J.P. Morgan Securities LLC, Morgan Stanley & Co. LLC and RBS Securities Inc. as representatives of the several Underwriters named in the Underwriting Agreement (the “Underwriters”), on the other hand.

In so acting, we have examined originals or copies certified or otherwise identified to our satisfaction of (i) the Registration Statement, (ii) the Base Prospectus, (iii) the Prospectus Supplement, (iv) the Indenture, (v) the Notes, (vi) the Underwriting Agreement, (vii) such certificates of officers of the Company, and the originals (or copies thereof, certified to our satisfaction) of such corporate documents and records of the Company and (viii) such other documents, records and papers as we have deemed relevant in order to give the opinions hereinafter set forth. In this connection, we have assumed the genuineness of signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals and the conformity to authentic original documents of all documents submitted to us as certified, conformed, facsimile or photostatic copies. In addition, we have relied, to the extent that we deem such reliance proper, upon such certificates of public officials and of officers of the Company with respect to the accuracy of material factual matters contained therein which we have not independently established.

Based upon the foregoing, it is our opinion that the Notes have been duly authorized, executed and delivered by the Company and, when duly authenticated by the Trustee in accordance with the terms of the Indenture and delivered to and paid for by the Underwriters in accordance with the terms of the Underwriting Agreement, will constitute valid and binding obligations of the

Company entitled to the benefits provided by the Indenture, except as the enforcement thereof may be limited by bankruptcy, insolvency, reorganization, moratorium or other similar laws relating to or affecting the rights and remedies of creditors or by general equitable principles (whether applied by a court of law or equity).

With your consent, we have assumed (a) that the Indenture has been authorized, executed and delivered by the parties thereto, (b) that the Indenture constitutes the valid, binding and enforceable obligation of the parties thereto other than the Company, enforceable against such parties in accordance with its terms and (c) the Trustee is in compliance, generally and with respect to acting as Trustee under the Indenture, with all applicable laws and regulations.

We do not express or purport to express any opinions with respect to laws other than the laws of the State of New York and the General Corporation Law of the State of Delaware (including applicable provisions of the Delaware Constitution and reported judicial decisions interpreting the foregoing).

We consent to the filing of this opinion as an exhibit to a Current Report on Form 8-K and its incorporation by reference into the Registration Statement and to the reference to our firm appearing under the caption “Legal Matters” in the Prospectus forming part of the Registration Statement. 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 Act or the rules and regulations of the Commission promulgated thereunder.

The opinions set forth in this letter are effective as of the date hereof. We do not undertake to advise you of any changes in our opinion expressed herein resulting from matters that may arise after the date of this letter or that hereinafter may be brought to our attention. We express no opinions other than as herein expressly set forth, and no opinion may be inferred or implied beyond that expressly stated herein.