Exhibit 5.1

98 SAN JACINTO BLVD. SUITE 1500 AUSTIN, TEXAS 78701-4078 TEL   +1 512.322.2500 FAX  +1 512.322.2501 www.bakerbotts.com AUSTIN BEIJING DALLAS DUBAI HONG KONG HOUSTON LONDON MOSCOW NEW YORK PALO ALTO RIYADH WASHINGTON

May 15, 2015

EQT GP Holdings, LP

625 Liberty Avenue, Suite 1700

Pittsburgh, Pennsylvania 15222

Ladies and Gentlemen:

We have acted as counsel to EQT GP Holdings, LP, a Delaware limited partnership (the “Partnership”), and EQT GP Services, LLC, a Delaware limited liability company and the general partner of the Partnership, with respect to certain legal matters in connection with the Registration Statement on Form S-8 (the “Registration Statement”) to be filed by the Partnership with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to 2,000,000 common units representing limited partner interests of the Partnership (the “Common Units”) that may be issued pursuant to the EQT GP Services, LLC 2015 Long-Term Incentive Plan (as amended from time to time, the “Plan”). At your request, this opinion is being furnished to you for filing as Exhibit 5.1 to the Registration Statement.

In our capacity as your counsel in the connection referred to above, we have examined such statutes, including the Delaware Revised Uniform Limited Partnership Act (the “Delaware LP Act”), and the Partnership’s records and documents, certificates of representatives of the Partnership and public officials, and other instruments and documents as we deemed necessary or advisable for the purposes of this opinion. In giving the opinion set forth below, we have relied, without independent investigation or verification, to the extent we deemed appropriate, upon the certificates, statements or other representations of officers or other representatives of the general partner of the Partnership and public officials, with respect to the accuracy of the factual matters contained in or covered by such certificates, statements or representations. In making our examination, we have assumed (i) that all signatures on all documents examined by us are genuine, all documents submitted to us as originals are authentic and complete and all documents submitted to us as copies are true and correct copies of the originals of such documents and (ii) that the Plan, the Partnership’s Certificate of Limited Partnership and the Partnership’s First Amended and Restated Agreement of Limited Partnership, each in substantially the form attached as an exhibit to the Registration Statement, will have been duly executed and delivered by the Partnership and the other parties thereto.

Based upon the foregoing, and subject to the assumptions, limitations and qualifications set forth herein, we are of the opinion that, when issued and delivered by the Partnership against payment therefor from time to time in accordance with the provisions of the Plan, the Common Units will be validly issued, fully paid and nonassessable.

The foregoing opinion is limited in all respects to the Delaware LP 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 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.

Very truly yours,

/s/ Baker Botts L.L.P.

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