Crabbe drained 4-of-7 three-point tries and Justin Cobbs ended with 21 points, including a game-sealing layup late in the second half for the Golden Bears (14-9, 6-5 Pac 12).
The surprising win was the third victory in four games for California.
Mark Lyons provided 16 points for the Wildcats (20-3, 8-3), whose four-game winning streak was snapped.
Solomon Hill also reached double figures with 13 points for Arizona.
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