Perkins secured the win with Gonzaga leading 78-77 when he gathered the rebound of his intentionally missed free throw with 2.5 seconds left. He went back to the line with 0.4 seconds left to make 1 of 2 for the final score.
Kyle Wiltjer had 20 points, Eric McClellan scored 15 and Domantas Sabonis added 11 for the Bulldogs (11-3, 3-0 West Coast Conference).
Gonzaga made four straight field-goal attempts to lead 73-69 on Wiltjer's jumper with 1:53 left. Jared Brownridge quickly answered with a 3-pointer to get Santa Clara (4-11, 0-3) within one, but Gonzaga made five of its next six free throws to hold the lead.
Brownridge finished 6 of 9 from 3-point range with 26 points. KJ Feagin scored 15 and Kai Healy added 10.