Exhibits 5.1 and 23.1

April 6, 2018

SS&C Technologies Holdings, Inc.

80 Lamberton Road

Windsor, CT 06095

Ladies and Gentlemen:

SS&C Technologies Holdings, Inc., a Delaware corporation (the “Company”), has filed with the Securities and Exchange Commission a Registration Statement on Form S-3 (File No. 333-205026) (the “Registration Statement”) for the purpose of registering under the Securities Act of 1933, as amended (the “Securities Act”), certain securities, including the 30,262,250 shares of its common stock, par value $0.01 per share (the “Securities”) to be sold pursuant to the Underwriting Agreement dated April 3, 2018 (the “Underwriting Agreement”) among the Company and the several underwriters named therein (the “Underwriters”). The Securities include 3,947,250 shares with respect to which the Underwriters have exercised their option to purchase pursuant to the Underwriting Agreement.

We, as your counsel, have examined originals or copies of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary or advisable for the purpose of rendering this opinion.

In rendering the opinion expressed herein, we have, without independent inquiry or investigation, assumed that (i) all documents submitted to us as originals are authentic and complete, (ii) all documents submitted to us as copies conform to authentic, complete originals, (iii) all signatures on all documents that we reviewed are genuine, (iv) all natural persons executing documents had and have the legal capacity to do so, (v) all statements in certificates of public officials and officers of the Company that we reviewed were and are accurate and (vi) all representations made by the Company as to matters of fact in the documents that we reviewed were and are accurate.

Based on the foregoing, we advise you that, in our opinion, when the Securities have been issued and delivered against payment therefor in accordance with the terms of the Underwriting Agreement, the Securities will be validly issued, fully paid and non-assessable.

We are members of the Bar of the State of New York and the foregoing opinion is limited to the laws of the State of New York and the General Corporation Law of the State of Delaware.

We hereby consent to the filing of this opinion as an exhibit to a report on Form 8-K to be filed by the Company on the date hereof and its incorporation by reference into the Registration Statement and further consent to the reference to our name under the caption “Legal Matters” in the prospectus supplement, which is a part of the Registration Statement. In giving this consent, we do not admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Davis Polk & Wardwell LLP