Austin Seferian-Jenkins caught eight passes for 154 yards and a touchdown for the Huskies (5-4, 3-3 Pac-12), who had been outscored 145-41 in three road games this season and had lost six straight away games since beating Utah on Oct. 1, 2011.
The Golden Bears (3-7, 2-5) lost for the fourth time in six games at their renovated stadium and are assured of missing out on a bowl for the second time in three seasons. That will only raise more questions about the status of coach Jeff Tedford, who has a 23-25 record since the start of the 2009 season.
Cal played the game without injured star receiver Keenan Allen and then lost starting quarterback Zach Maynard to a left knee injury late in the fourth quarter.
Backup Allan Bridgford drove the Bears to the 25 with just over a minute left but he missed C.J. Anderson down the sideline on fourth-and-5 to end Cal's hopes.
Each team had four turnovers in a sloppy game, including three lost fumbles in a span of six plays early in the fourth quarter. An interception on the next drive helped seal the win for Washington.
Shaq Thompson intercepted a pass by Maynard near midfield and returned it 33 yards to the Cal 28. Making that play even more painful for the Bears was the fact that Thompson originally committed to play at Cal before changing his mind when top recruiter Tosh Lupoi left for Washington just weeks before signing day.
Sankey ran four straight plays and scored from 1-yard out to give the Huskies a 21-13 lead. Washington now needs just one win in its final three games against the bottom teams in the conference, Utah, Colorado and Washington State, to become bowl eligible.
Cal settled for field goals twice in the third quarter after driving deep into Washington territory, which proved costly when Seferian-Jenkins made a leaping grab over the smaller Steve Williams for a 29-yard score on third-and-goal to give the Huskies a 14-13 lead in the final minute of the third quarter.
The score remained there when Cal failed to capitalize on another good chance. Maynard overthrew an open Chris Harper in the end zone and D'Amato missed wide right from 41 yards, ending a streak of 11 straight makes.
Both teams had little trouble moving the ball in the first half but struggled to get it into the end zone. Washington scored on Sankey's 4-yard run on its second drive of the game but came up empty on three other trips into Cal territory. Sankey was stopped on fourth-and-1 twice in the first half and Price was intercepted by Nick Forbes in the closing seconds on third-and-5 from the 9.
The Bears also squandered good scoring chances with Isi Sofele losing a fumble at the Washington 21 on their first drive of the game and Bigelow losing a fumble at the 11 on the second drive.
Cal scored late in the second quarter on Harper's 14-yard reverse on a drive extended by a personal foul on Danny Shelton on third-and-long.