The winning kick was Frisina's third field goal of the game for Boise State (11-2), which iced the victory when Jeremy Iaone intercepted Washington's Keith Price with 14 seconds remaining.
Joe Southwick completed 26-of-38 passes for 267 yards and hooked up with tight end Holden Huff on two touchdown passes for the Broncos.
The Huskies (7-6) staged a comeback in which they rallied from a 15-point first-half deficit to take a 26-25 lead with 4:09 to go, but wound up on the losing end.
Price mustered 242 aerial yards with a touchdown on 20-of-39 efficiency and also ran for a score, but was intercepted twice in the setback.
Bishop Sankey rambled for 205 rushing yards with a touchdown on 30 carries for the Huskies.