Exhibit 5.1

910 Louisiana Street Houston, Texas 77002-4995   TEL +1 713.229.1234 FAX +1 713.229.1522 BakerBotts.com

AUSTIN BRUSSELS DALLAS DUBAI HOUSTON LONDON

NEW YORK PALO ALTO RIYADH SAN FRANCISCO SINGAPORE WASHINGTON

May 14, 2025

CenterPoint Energy, Inc.

1111 Louisiana

Houston, Texas 77002

Ladies and Gentlemen:

As set forth in the Post-Effective Amendment No. 2 (the "Post-Effective Amendment") to the Registration Statement on Form S-8 (File No. 333-159586) 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 2,784,715 shares (the “Shares”) of common stock, par value $0.01 per share, of the Company (“Common Stock”) issuable pursuant to the CenterPoint Energy, Inc. 2022 Long Term Incentive Plan (the “2022 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 Post-Effective Amendment.

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, Amended and Restated Bylaws, Third Amended and Restated Bylaws and Fourth Amended and Restated Bylaws, each as amended to date, the CenterPoint Energy, Inc. 2009 Long Term Incentive Plan, the 2022 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, in the case of Shares originally issued by the Company pursuant to the provisions of the 2022 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 2022 Plan, the Shares 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 such award for the consideration established pursuant to the terms of the 2022 Plan and otherwise in accordance with the terms and conditions of such award, including, if applicable, the lapse of any restrictions relating thereto, the satisfaction of any performance conditions associated therewith and any requisite determinations by or pursuant to the authority of the Board as provided therein, and, in the case of stock options, the exercise thereof and payment for such Shares as provided therein, such Shares will be validly issued, fully paid and non-assessable.

The opinions set forth above in this opinion 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 opinion 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 with the Commission as Exhibit 5.1 to the Post-Effective Amendment. 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.