Exhibit 5.1

December 2, 2016

EOG Resources, Inc.

1111 Bagby, Sky Lobby 2

Houston, Texas 77002

Re: EOG Resources, Inc.

Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to EOG Resources, Inc., a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-3 (the “Registration Statement”), filed by the Company with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Act”). The Registration Statement relates to the offer and sale by certain selling stockholders of the Company (the “Selling Stockholders”) named in the Registration Statement of up to 25,203,773 shares (the “Shares”) of the Company’s common stock, par value $0.01 per share. The Shares may be issued and sold or delivered from time to time as set forth in the Registration Statement, any amendment thereto, the prospectus contained therein (the “Prospectus”) and supplements to the Prospectus pursuant to Rule 415 under the Act. This opinion is being furnished at the request of the Company and 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, and the conformity to authentic original documents of all copies submitted to us as conformed, certified or reproduced copies. We have also assumed that, upon sale and delivery, valid book-entry notations for the issuance of the Shares in uncertificated form were duly made in the share register of the Company. As to various questions of fact relevant to this letter, we have relied, without independent investigation, upon certificates of public officials and certificates of officers of the Company, all of which 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 the Shares are duly authorized, validly issued, fully paid and non-assessable.

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

EOG Resources, Inc. December 2, 2016 Page 2

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

B. 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.

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EOG Resources, Inc. December 2, 2016 Signature Page

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the use of our name in the Prospectus 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.

Very truly yours,

/s/ AKIN GUMP STRAUSS HAUER & FELD LLP

AKIN GUMP STRAUSS HAUER & FELD LLP