Exhibit 5.1

Nevro Corp.

4040 Campbell Avenue

Menlo Park, CA 94025

Re: Form S-1 Registration Statement File No. 333-204270

Public Offering of up to an aggregate of 3,934,681 Shares of Common Stock of Nevro Corp.

Ladies and Gentlemen:

We have acted as special counsel to Nevro Corp., a Delaware corporation (the “Company”), in connection with the proposed registration of up to 1,475,506 shares of common stock, $0.001 par value per share (“Common Stock”) by the Company (the “Company Shares”) and up to 2,459,175 shares of Common Stock by the selling stockholders identified in the Registration Statement (as defined herein) (the “Selling Stockholder Shares” and, together with the Company Shares, the “Shares”). The Shares are included in a registration statement on Form S–1 under the Securities Act of 1933, as amended (the “Act”), filed with the Securities and Exchange Commission (the “Commission”) on May 18, 2015 (Registration No. 333-204270) (as amended, the “Registration Statement”). This opinion is being furnished in connection with the requirements of Item 601(b)(5) of Regulation S-K under the Act, and no opinion is expressed herein as to any matter pertaining to the contents of the Registration Statement or related prospectus (the “Prospectus”), other than as expressly stated herein with respect to the issue of the Shares.

As such counsel, we have examined such matters of fact and questions of law as we have considered appropriate for purposes of this letter. With your consent, we have relied upon certificates and other assurances of officers of the Company and others as to factual matters without having independently verified such factual matters. We are opining herein as to the General Corporation Law of the State of Delaware (the “DGCL”), and we express no opinion with respect to any other laws.

June 1, 2015

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Subject to the foregoing and the other matters set forth herein, it is our opinion that, as of the date hereof, (i) when the Company Shares shall have been duly registered on the books of the transfer agent and registrar therefor in the name or on behalf of the purchasers and have been issued by the Company against payment therefor in the circumstances contemplated by the form of underwriting agreement most recently filed as an exhibit to the Registration Statement, the issue and sale of the Company Shares will have been duly authorized by all necessary corporate action of the Company, and the Company Shares will be validly issued, fully paid and nonassessable, and (ii) the Selling Stockholder Shares have been duly authorized, validly issued, fully paid and nonassessable. In rendering the foregoing opinion we have assumed that the Company will comply with all applicable notice requirements under the DGCL.

This opinion is for your benefit in connection with the Registration Statement and may be relied upon by you and by persons entitled to rely upon it pursuant to the applicable provisions of the Act. We consent to your filing this opinion as an exhibit to the Registration Statement and to the reference to our firm in the Prospectus under the heading “Legal Matters.” In giving such consent, we do not thereby 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.