Jack, who alternated between offense and defense due to injuries in the UCLA backfield, ran 66 yards for what turned out to be the game-winning touchdown as the Bruins (7-2, 4-2 Pac-12) took a second straight.
Brett Hundley tossed two TDs to Shaquelle Evans and ran for another score, racking up 283 yards of total offense.
B.J. Denker made good on 20-of-33 passes for 186 yards with two scoring strikes to Nate Phillips but also hurled an interception that killed a comeback try for the Wildcats (6-3, 3-3).
Ka'Deem Carey rolled up 149 rushing yards with a score as Arizona's three-game winning streak was snapped.