Cal led by as many as 15 points midway through the second half, but the Utes pulled within 58-55 on Jason Washburn's 3-pointer with 55 seconds remaining.
David Kravish missed at the other end for the Golden Bears (11-7, 3-3 Pac-12) but poked the rebound out to Crabbe, who was fouled and sank two free throws with 17 seconds left.
Freshman Brandon Taylor missed a 3-pointer with 11 seconds left for the Utes (9-10, 1-6), and Justin Cobb grabbed the rebound and sank a pair of free throws to seal the win for Cal.
Cal used a 13-0 run midway through the first half to take a commanding lead.
Utah shot better from the floor than Cal did but committed 17 turnovers, including six by Jordan Loveridge.
More Sports Headlines
Chum fishery set to close in Marine Area 10 No. 10 Gonzaga rolls past Washington 80-64 in Bahamas Huskies wary of Cougars' running game and defense Seahawks RB Lynch out multiple weeks after abdominal surgery M’s notebook: Hultzen clear waivers, sent to Triple-A Ex-Cowboys RB Randle arrested at Kansas casino Broncos bring in Ponder to add depth at QB NHLís Canadiens sign GM Bergevin to extension
Our new comment system is not supported in IE 7. Please upgrade your browser here.