Sanadze, who finished with 15 points, was 5-of-6 from the free-throw line on the game, with the last four attempts coming in the final 3 seconds. The first put the Toreros ahead 67-63 but Gonzaga charged down the court and David Stockton made a 3-point shot with 0.5 seconds to play.
The Bulldogs immediately fouled Sanadze, who made the clinching free throws for San Diego (16-14, 7-11 West Coast Conference). It was the first time San Diego had beaten Gonzaga since March 10, 2008.
It was the second loss this week for Gonzaga (23-6, 13-3 WCC), which locked up a tie for the conference regular-season title a week ago. The Bulldogs have two games left to claim the outright WCC championship.
Sanadze finished with 15 points and Johnny Dee led San Diego with 16.
Gonzaga got a game-high 18 points and 15 rebounds from San Dower and Przemek Karnowski added 17 points.