Hundley completed 16-of-24 passes for 294 for the Bruins (2-0), who scored 38 unanswered points in the game and outscored Nebraska (2-1) 31-0 in the second half.
The defeat ended Nebraska's home winning streak at 10 games.
Jordan James ran the ball 22 times for 105 yards and a touchdown for UCLA. Shaquelle Evans caught three passes for 97 yards and a touchdown.
Taylor Martinez three touchdown passes for Nebraska in the first half that at one point had the Cornhuskers up 21-3. Ameer Abdullah ran for 98 yards on 23 carries.