Exhibit 5.1

June 25, 2018

EQT Midstream Partners, LP

625 Liberty Avenue, Suite 1700

Pittsburgh, Pennsylvania 15222

Ladies and Gentlemen:

We have acted as counsel to EQT Midstream Partners, LP, a Delaware limited partnership (the “Partnership”), in connection with the proposed offering and sale by the Partnership of an aggregate of $2,500 million of its senior notes consisting of $1,100 million aggregate principal amount of its 4.750% Senior Notes due 2023 (the “2023 Notes”), $850 million aggregate principal amount of its 5.500 % Senior Notes due 2028 (the “2028 Notes”), and $550 million aggregate principal amount of its 6.500% Senior Notes due 2048 (the “2048 Notes” and, together with the 2023 Notes and the 2028 Notes, the “Notes”) pursuant to that certain Underwriting Agreement dated June 20, 2018 (the “Underwriting Agreement”) by and among the Partnership and EQT Midstream Services, LLC, a Delaware limited liability company (the “General Partner”), on the one hand, and Merrill Lynch, Pierce, Fenner & Smith Incorporated, Wells Fargo Securities, LLC, Deutsche Bank Securities Inc., and PNC Capital Markets LLC, as representative of the underwriters named in Schedule I thereto, on the other.

The Notes are to be issued pursuant to an Indenture (the “Base Indenture”), dated August 1, 2014, by and among the Partnership, certain subsidiaries of the Partnership parties thereto and The Bank of New York Mellon Trust Company, N.A., as trustee (the “Trustee”), as supplemented and amended by (i) in the case of the 2023 Notes, the Third Supplemental Indenture dated as of the date hereof (the “Third Supplemental Indenture”), (ii) in the case of the 2028 Notes, the Fourth Supplemental Indenture, dated as of the date hereof (the “Fourth Supplemental Indenture”) and (iii) in the case of the 2048 Notes, the Fifth Supplemental Indenture dated as of the date hereof (the “Fifth Supplemental Indenture” and, together with the Third Supplemental Indenture and the Fourth Supplemental Indenture, the “Supplemental Indentures”), each by and between the Partnership and the Trustee (the Base Indenture, as so supplemented and amended by the Supplemental Indentures, the “Indenture”).

In connection with this opinion, we have examined and relied upon the accuracy of original, certified copies or photocopies of such records, agreements, certificates and other documents as we have deemed necessary or appropriate to enable us to render the opinions set out below, including (i) the Registration Statement on Form S-3 (Registration No. 333-212362) (as amended, the “Registration Statement”) filed by the Partnership with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”); (ii) the prospectus included in the Registration Statement dated June 30, 2016 (the “Base Prospectus”); (iii) the prospectus supplement to the Base Prospectus dated June 20, 2018 and filed with the Commission on June 21, 2018 (together with the Base Prospectus, the “Prospectus”); (iv) the Indenture; (v) the Underwriting Agreement; (vi) the Delaware Revised Uniform Limited Partnership Act (the “Delaware LP Act”); (vii) the Delaware Limited Liability Company Act (the “Delaware LLC Act”); (viii) the Partnership’s records and documents, certificates of representatives of the Partnership, the General Partner and public officials; (ix) statutes; and (x) other instruments and documents as we deemed necessary or advisable for the purposes of this opinion.

In making our examination, we have assumed that all signatures on documents examined by us are genuine, that all documents submitted to us as originals are authentic and complete, that all documents submitted to us as certified or photostatic copies conform with the original copies of such documents and that all information submitted to us was accurate and complete.  In addition, we have relied, without independent investigation, upon the factual accuracy of the representations and warranties contained in the certificates we examined. We have also assumed that the Notes will be issued and sold in the manner set forth in the Prospectus and the Underwriting Agreement and that any certificates representing the Notes will be duly executed and delivered by the Trustee.

Based on the foregoing, and subject to the assumptions, limitations and qualifications set forth herein, we are of the opinion that when the Notes have been duly executed, issued, and authenticated in accordance with the terms of the Indenture and delivered against payment therefor in the circumstances contemplated by the Underwriting Agreement, the Notes will have been duly

authorized by all necessary limited partnership action of the Partnership, and the Notes will be legally valid and binding obligations of the Partnership, enforceable against the Partnership in accordance with their terms, except as the enforceability thereof may be limited by (a) applicable bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium or other laws relating to or affecting creditors’ rights and remedies generally and general principles of equity (regardless of whether such enforceability is considered in a proceeding in equity or at law) and (b) public policy, applicable law relating to fiduciary duties and indemnification and contribution and an implied covenant of good faith and fair dealing.

The foregoing opinion is limited in all respects to the relevant law of the State of New York, the Delaware LP Act and the Delaware LLC Act, as published in effect on the date hereof, and applicable reported judicial decisions, rules and regulations interpreting and implementing those laws.  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 Partnership’s Current Report on Form 8-K dated on or about the date hereof, to the incorporation by reference of this opinion into the Registration Statement and to the reference to our firm under the caption “Legal Matters” in the Prospectus forming a 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 Securities Act or the rules and regulations of the Commission thereunder.

The opinion expressed herein is given as of the date hereof and we undertake no obligations to supplement this opinion if any applicable law changes after such date or if we become aware of any facts that might change the opinion expressed herein after such date or for any other reason.

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