Washington (17-12, 10-8 Pac 12) used a 9-0 run midway through the first half, including a 3-pointer by Plum, to take a 36-32 lead at the break.
The Huskies led by as much as 10 in the second half, but Cal (21-8, 13-5) cut its deficit to three with 33 seconds left on a pair of free throws and a layup by Reshanda Gray, who finished with 16 points and 16 rebounds.
The Bears missed their last two shots and two free throws though as Washington escaped with the mild upset.
Talia Walton had 12 points for Washington, which bounced back from consecutive losses to Oregon State and highly-ranked Stanford.
Afure Jemerigbe led California with 24 points, including five 3-pointers, and six assists.