Parker Van Dyke scored a career-high 18 points and Tyler Rawson added 12 for the Utes. Utah (18-9, 10-6 Pac-12) won its fifth straight game.
Aaron Holiday scored 23 points and Thomas Welsh added 15 to lead the Bruins. UCLA (19-9, 10-6 Pac-12) rallied from a double-digit deficit, but could not overtake the Utes in the final two minutes.
The Bruins made five consecutive shots to jump in front and eventually went ahead 22-15 on back-to-back baskets from Prince Ali and Alex Olesinski. Utah reclaimed some momentum by forcing three straight turnovers. The Utes finally took their first lead at 29-26 when Donnie Tillman buried a 3-pointer and followed up with a dunk.