Sanchez, who scored 15 points in the second half, had 12 of Boise State's 14 points in one stretch that gave the Broncos a 65-61 lead with 5:53 left in the game.
Kurt Cunningham scored consecutive baskets for Boise State (8-3) for a 69-61 lead with 3:06 remaining. San Diego (6-7) then cut the lead to three on three occasions, the final time on Trumaine Johnson's layup with 7.6 seconds left. But after the Toreros forced a turnover, Danny Brown missed a 3-pointer at the buzzer.
Gyno Pomare scored a game-high 22 points for San Diego and Johnson added 16.