Mikayla Cowling's pull-up jumper put Cal up 69-68 with 2:40 remaining, but the Bruins responded with six consecutive points, going up 74-69 on two free throws by Canada with 38 seconds left.
Cowling had 16 points and Asha Thomas and Kristine Anigwe added 15 apiece for Cal (21-10). Kelli Hayes and Monique Billings each added 18 points for UCLA.
The Bears, who won six of their final seven regular-season games, opened the fourth quarter with a 7-2 run, taking a 62-55 lead on a rebound putback by CJ West. UCLA capitalized on two turnovers to answer with 10 consecutive points to go back in front 65-62.