White racked up 109 rushing yards on 15 carries, scoring four times, and also added a 3-yard touchdown pass to Sam Arneson as the Badgers (8-5, 5-4 Big Ten) qualified for their third straight Rose Bowl.
Ball added three TDs en route to 202 yards on 21 tries and Curt Phillips completed 6-of-8 passes for 71 yards for Wisconsin, which will meet Pac-12 champs Stanford Jan. 1.
The Badgers were playing in the Big 10 title game thanks to the NCAA suspensions of Ohio State and Penn State.
The Cornhuskers (10-3, 7-2), meanwhile, saw their six-game winning streak snapped as Taylor Martinez was picked off twice.
The Nebraska quarterback threw for 184 yards on 17-of-33 efficiency while also carrying the ball 19 times for 140 yards and two scores.