Thomas -- who was coming off a 31-point performance in the second round -- hauled down seven rebounds while Jared Sullinger added 18 points, including two key baskets late, for the No. 2 seed Buckeyes (29-7).
Aaron Craft supplied 17 points and 10 assists as Ohio State advanced to play the winner of Sunday's contest between Florida State and Cincinnati in the East Region semifinals.
Seventh-seeded Gonzaga (26-7) was led by Gary Bell Jr. with 18 points, five assists and four rebounds.
Elias Harris contributed 16 points and seven rebounds in the Bulldogs' loss.