Devin Lucien turned a short pass into a 40-yard TD with 9:57 to play, and the Bruins (8-2, 5-2 Pac-12) got creative to hold off a lively challenge from the Huskies (6-4, 3-4), who lost starting quarterback Keith Price to a shoulder injury right before halftime.
Jack followed up his 120-yard debut at running back last week by becoming the 13th player in UCLA history to score four touchdowns.
Cyler Miles passed for 149 yards after replacing Price, but the Huskies have lost nine of their last 12 Pac-12 road games.