Patrick Christopher and Theo Robertson added 17 points apiece for the Golden Bears (7-2), but Christopher nearly cost Cal the victory.
His intentional foul on Utah's Carlon Brown with just under a minute left in the game allowed the Utes to score three straight points and tie the game 69-69 with 40 seconds left.
Cal ran down most of the clock before Randle hit the game-winning shot.
Luke Nevill led Utah (5-3) with 18 points, while Tyler Kepkay added 17 and Brown had 15.
The Utes, who defeated Cal last season in the last second, played without starting point guard Luka Drca, who was out with a sprained ankle.