Exhibit 5.1

May 27, 2014

Arista Networks, Inc.

5453 Great America Parkway

Santa Clara, CA 95054

Ladies and Gentlemen:

This opinion is furnished to you in connection with the Registration Statement on Form S-1 (Registration No. 333-194899), as amended (the “Registration Statement”), filed by Arista Networks, Inc. (the “Company”) with the Securities and Exchange Commission in connection with the registration under the Securities Act of 1933, as amended, of 6,037,500 shares (including up to 787,500 shares issuable upon exercise of an option granted to the underwriters by the Company) of the Company’s common stock, $0.0001 par value per share (the “Shares”), to be issued and sold by the Company. We understand that the Shares are to be sold to the underwriters for resale to the public as described in the Registration Statement and pursuant to an underwriting agreement, substantially in the form filed as an exhibit to the Registration Statement, to be entered into by and among the Company and the underwriters (the “Underwriting Agreement”).

We are acting as counsel for the Company in connection with the sale of the Shares by the Company. In such capacity, we have examined originals or copies, certified or otherwise identified to our satisfaction, of such documents, corporate records, certificates of public officials and other instruments as we have deemed necessary for the purposes of rendering this opinion. In our examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity with the originals of all documents submitted to us as copies, the authenticity of the originals of such documents and the legal competence of all signatories to such documents.

We express no opinion herein as to the laws of any state or jurisdiction other than the General Corporation Law of the State of Delaware (including the statutory provisions and all applicable judicial decisions interpreting those laws) and the federal laws of the United States of America.

On the basis of the foregoing, we are of the opinion, that the Shares to be issued and sold by the Company have been duly authorized and, when such Shares are issued and paid for in accordance with the terms of the Underwriting Agreement, will be validly issued, fully paid and nonassessable.

We consent to the use of this opinion as an exhibit to the Registration Statement, and we consent to the reference of our name under the caption “Legal Matters” in the prospectus forming part of the Registration Statement.

AUSTIN     BEIJING     BRUSSELS     GEORGETOWN, DE     HONG KONG     LOS ANGELES     NEW YORK

PALO ALTO     SAN DIEGO     SAN FRANCISCO     SEATTLE     SHANGHAI     WASHINGTON, DC

May 27, 2014

Page 2