Giorgio Tavecchio booted a career-long 53-yard field goal with one second remaining to account for the game's only score.
It was a wild, and somewhat-foolish final 1:05 for the Huskies, who ran two conservative Jesse Callier runs before Cal called timeout.
On third down, Jake Locker threw the ball away to stop the clock, and the Bears got it back at their own 34-yard line with 17 seconds to go.
Brock Mansion, who had done very little through the air, completed a 21-yard pass to Keenan Allen.
With seven seconds remaining, Mansion then connected with Michael Calvin along the left sideline. The receiver was kept up, and time looked to have expired.
But referee Larry Farina ruled Cal called timeout with time still remaining, and put the second back on the clock - giving Tavecchio a chance at a long field goal.
After the half concluded, UW coach Steve Sarkisian went on the field to get an ruling explanation from Farina before heading off to the locker room.
On three drives in the second quarter, the UW got into Bears' territory. Twice, turnovers - a Callier fumble and a Locker interception - did the Huskies in.
Locker is 8-of-14 for 52 yards.