Gonzaga led by nine points heading into the game's final five minutes, but the Broncos rallied to take the lead with 28 seconds to go on a jump shot by Brandon Clark.
Dower then ended Santa Clara's upset hopes with his long-range shot that boosted the Bulldogs to 19-3 for the season and to 9-1 atop the West Coast Conference.
Gary Bell led Gonzaga with 15 points and Dower had 13. The 3-point attempt Dower made at game's end was the only one he tried during the entire contest.
Santa Clara (10-13, 3-7 WCC) was led by 15 points from Evan Roqemore.