Junzag’s basket in the lane with 54 seconds left gave UCLA a 61-57 lead. Erik Stevenson answered with a 3 for Washington, but Jules Bernard hit a jumper from the top of the lane with nine seconds left to push the lead to three.
After each team split free throws, Quade Green missed a desperation 3-pointer at the buzzer trying to force overtime.
Bernard finished with 14 points for the Bruins, the only other player in double figures. UCLA (14-5, 10-3 Pac-12) had lost its previous two and three of four after starting conference play 8-0.
Marcus Tsohonis led Washington (3-16, 2-12) with 22 points off the bench, all coming in the second half.