Exhibit 5.1

910 LOUISIANA
HOUSTON, TEXAS
77002-4995   TEL  +1 713.229.1234 FAX +1 713.229.1522 BakerBotts.com AUSTIN BEIJING BRUSSELS DALLAS DUBAI HONG KONG HOUSTON LONDON MOSCOW NEW YORK PALO ALTO RIYADH SAN FRANCISCO WASHINGTON

May 29, 2020

CenterPoint Energy, Inc.

1111 Louisiana

Houston, Texas 77002

Ladies and Gentlemen:

As set forth in the Registration Statement on Form S-8 (the “Registration Statement”) to be filed on the date hereof by CenterPoint Energy, Inc., a Texas corporation (the “Company”), with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to 350,000 shares (the “Shares”) of common stock, par value $0.01 per share, of the Company (the “Common Stock”) issuable pursuant to the Amended and Restated CenterPoint Energy, Inc. Stock Plan for Outside Directors (as amended, the “Plan”), certain legal matters in connection with the Shares subject to original issuance by the Company therewith are being passed upon for you by us. At your request, this opinion letter 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 originals, or copies certified or otherwise identified, of the Company’s Restated Articles of Incorporation and Third Amended and Restated Bylaws, each as amended to date, the Plan, corporate records of the Company, including minute books of the Company, as furnished to us by you, certificates of public officials and of representatives of the Company, statutes and other instruments and documents as a basis for the opinions hereinafter expressed. In giving such opinions, we have relied, to the extent we deem appropriate without independent investigation or verification, upon certificates of officers of the Company and of public officials with respect to the accuracy of the material factual matters contained in such certificates. In giving the opinions below, we have assumed that the signatures on all documents examined by us are genuine, that all documents submitted to us as originals are accurate and complete, that all documents submitted to us as copies are true, correct and complete copies of the originals thereof and that all information submitted to us is accurate and complete. In addition, we have assumed for purposes of this opinion letter that the consideration received by the Company for the Shares will not be less than the par value of the Shares.

On the basis of the foregoing, and subject to the assumptions, limitations and qualifications set forth herein, we are of the opinion that:

1. In the case of Shares originally issued by the Company pursuant to the provisions of the Plan following due authorization of a particular award thereunder by the Board of Directors of the Company or a duly constituted and acting committee thereof (the “Board”) as provided in and in accordance with the Plan, the Shares

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issuable pursuant to such award will have been duly authorized by all necessary corporate action on the part of the Company. Upon issuance and delivery of such Shares from time to time pursuant to the terms of the Plan and such award at the end of the applicable Restriction Period as defined in and established under the Plan, for the consideration fixed by the Board, including services provided by the director to whom the Shares are issued and the other benefits to the Company contemplated by the Plan, such Shares will be validly issued, fully paid and nonassessable.

The opinions set forth above in this letter are limited to the original issuance of Shares by the Company and do not cover shares of Common Stock delivered by the Company out of shares reacquired by it.

The opinions set forth above in this letter are limited in all respects to matters of the laws of the State of Texas as in effect on the date hereof. We hereby consent to the filing of this opinion letter as Exhibit 5.1 to 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 thereunder.

Very truly yours,

/s/ BAKER BOTTS L.L.P.