Thomas' third scoring strike was an 11-yard pass to Lavasier Tuinei 3 seconds into the fourth quarter that put the Ducks (11-2) ahead for good at 42-38.
Alejandro Maldonado later added a 30-yard field goal for a seven-point lead and Wisconsin receiver Jared Abbrederis fumbled after a 29-yard catch on the ensuing drive, spoiling the Badgers' best chance to tie the contest.
De'Anthony Thomas added scoring runs of 91 and 64 yards for the Ducks, who won a BCS bowl game after losses to Auburn in last year's BCS Championship and to Ohio State in the 2010 Rose Bowl.
Tuinei made eight grabs for 158 yards and LaMichael James rolled up 159 yards on 25 carries with a score in the win.
Russell Williams passed for 296 yards and two TDs while Monte Ball gained 165 yards on 32 carries for Wisconsin (11-2), which dropped its second straight Rose Bowl.