Exhibit 5.1

[Letterhead of White & Case LLP]

September 28, 2016

Hess Corporation

1185 Avenue of the Americas

New York, New York 10036

Ladies and Gentlemen:

We have acted as counsel to Hess Corporation, a Delaware corporation (the “Company”), in connection with the issuance of $1,000,000,000 aggregate principal amount of the Company’s 4.30% Notes due 2027 and $500,000,000 aggregate principal amount of the Company’s 5.80% Notes due 2047 (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. 333-202379) (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, 2015, a Prospectus, dated February 27, 2015, forming part of the Registration Statement (the “Base Prospectus”), a Prospectus Supplement, dated September 19, 2016, 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 in accordance with the Underwriting Agreement dated September 19, 2016 (the “Underwriting Agreement”) among the Company, on the one hand, and Goldman, Sachs & Co., J.P. Morgan Securities LLC and Morgan Stanley & Co. LLC 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) the Restated Certificate of Incorporation of the Company, as amended on May 22, 2013, May 12, 2014 and February 4, 2016; (viii) the By-laws of the Company, as amended on November 4, 2015; (ix) the resolutions adopted by the Company’s board of directors (the “Board”) on September 7, 2016 and the pricing committee of the Board on September 19, 2016; and (x) such corporate records, agreements, documents and other instruments, and such certificates or comparable documents of public officials and of officers and representatives of the Company, and have made such inquiries of such officers and representatives, as we have deemed relevant and necessary as a basis for the opinion hereinafter set forth.

In such examination, we have assumed the genuineness of all signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as certified, conformed or photostatic copies, and the authenticity of the originals of such latter documents. As to all questions of fact material to this opinion that have not been independently established, we have relied upon certificates or comparable documents of public officials and officers and representatives of the Company, representations of the Company and documents furnished to us by the Company without independent verification of their accuracy.

September 28, 2016

Based on the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the 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 enforceability thereof may be limited by bankruptcy, insolvency (including, without limitation, all laws related to fraudulent transfers), reorganization, moratorium or other similar laws relating to or affecting enforcement of the rights and remedies of creditors or by general equitable principles (whether applied by a court of law or equity), including, without limitation, (x) the possible unavailability of specific performance, injunctive relief or any other equitable remedy and (y) concepts of materiality, reasonableness, good faith and fair dealing in the performance and enforcement of contracts.

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. Our opinion expressed above is subject to the qualification that we express no opinion as to the applicability of, compliance with, or effect of any laws except the laws of the State of New York and the General Corporation Law of the State of Delaware. This opinion shall be understood and interpreted in accordance with the customary practice of lawyers in New York who regularly give, and lawyers who on behalf of their clients regularly advise opinion recipients regarding, opinions of the kind set forth in this letter.

We hereby consent to the filing of this opinion with the Commission as Exhibit 5.1 to the Company’s Current Report on Form 8-K filed on September 28, 2016 and to the incorporation by reference of this opinion into the Registration Statement. We also hereby consent to the reference to our firm under the heading “Legal Matters” in the Registration Statement. In giving this consent, we do not hereby admit that we are in 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 hereafter 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.

DJ: EG: MD

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