Exhibit 5.1

Hess Midstream LP

1501 McKinney Street

Houston, Texas 77010

Ladies and Gentlemen:

We have acted as special counsel to Hess Midstream LP, a Delaware limited partnership (the “Company”), in connection with the offering and sale by certain selling shareholders of the Company (the “Selling Shareholders”) of up to 6,900,000 Class A shares representing limited partner interests in the Company (the “Shares”) issuable upon exchange of an equivalent number of Class B units representing limited partner interests (“Class B Units”) in Hess Midstream Operations LP (the “Operating Company”), together with a corresponding number of Class B shares representing limited partner interests (“Class B Shares”) in the Company as described in the Registration Statement. The Shares are included in a registration statement on Form S-3 under the Securities Act of 1933, as amended (the “Act”), filed by the Company with the Securities and Exchange Commission (the “Commission”) on December 20, 2019 (File No. 333-235650) (the “Registration Statement”), including a base prospectus, dated December 31, 2019 (the “Base Prospectus”), a preliminary prospectus supplement, dated 10, 2021, filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Preliminary Prospectus”), and a prospectus supplement, dated 10, 2021, filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Prospectus”). The Shares are being sold pursuant to an underwriting agreement, dated 10, 2021, among Hess Midstream GP LLC, a Delaware limited liability company (“HESM GP LLC”), Hess Midstream GP LP, a Delaware limited partnership (“HESM GP LP” and, together with HESM GP LLC, the “General Partner”), the Company, the Selling Shareholders and Goldman Sachs & Co. LLC, as representative of the several underwriters named in Schedule I thereto.

This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement, the Preliminary Prospectus or the Prospectus, other than as expressly stated herein with respect to the issue of the Shares.

March 15, 2021

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As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the General Partner and others as to factual matters without having independently verified such factual matters. We are opining herein as to the Delaware Revised Uniform Limited Partnership Act (the “DRULPA”) and we express no opinion with respect to any other laws.

Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof, upon the issuance and delivery of the Shares in exchange for an equivalent number of Class B Units and Class B Shares in accordance with the Amended and Restated Agreement of Limited Partnership of the Company and the Third Amended and Restated Agreement of Limited Partnership of the Operating Company, the Shares will be validly issued and, under the DRULPA, purchasers of the Shares will have no obligation to make further payments for their purchase of the Shares or contributions to the Company solely by reason of their ownership of the Shares or their status as limited partners of the Company, and no personal liability for the obligations of the Company, solely by reason of being limited partners of the Company.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Company’s Current Report on Form 8-K dated March 15, 2021 and to the reference to our firm contained in the Prospectus under the heading “Validity of the Class A Shares.” In giving such consent, we do not thereby 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 thereunder.

Very truly yours,

/s/ Latham & Watkins LLP