Exhibit 32.1

CERTIFICATIONS OF CHIEF EXECUTIVE OFFICER AND CHIEF FINANCIAL OFFICER

PURSUANT TO
18 U.S.C. SECTION 1350,
AS ADOPTED PURSUANT TO
SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report on Form 10-Q of Invuity, Inc. (the “Company”) on Form 10-Q for the fiscal quarter ending June 30, 2018, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), we, Scott Flora,  Interim President and Chief Executive Officer, and James Mackaness, Chief Financial Officer, of the Company, certify, pursuant to and for purposes of 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that to our knowledge:

(1) the Quarterly Report on Form 10-Q fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) the information contained in such Quarterly Report on Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ Scott Flora

Scott Flora

Interim President and Chief Executive Officer

August 3, 2018

/s/ James Mackaness

James Mackaness

Chief Financial Officer

August 3, 2018