After Tucker's clutch jumper ended a 60-60 deadlock, the Huskies' Nigel Williams-Goss misfired on a 3-point try on the ensuing possession and the ball landed out of bounds to Utah.
The Utes' Brandon Taylor then knocked down a pair of foul shots to extend the lead to five, with Dallin Bachynski later sealing Utah's victory by making two more free throws with two seconds to go.
Delon Wright led Utah (21-10) with 15 points, nine of which came in the second half, while Jordan Loveridge added 13 points and nine rebounds for the eighth- seeded Utes, who will next take on conference regular-season champion Arizona in Thursday's quarterfinals.
Washington (17-15) fought back from a 34-24 halftime deficit to take a 59-58 lead on 3-point plays from Williams-Goss and Desmond Simmons on back-to-back posssesions, the last coming with 1:23 left to play.
Darin Johnson finished with 16 points and Williams-Goss had 14 for the ninth- seeded Huskies. C.J. Wilson recorded 14 points in the loss, but shot just 4-of-15 from the floor.