The Ducks (9-4) scored 28 consecutive points in the third quarter to snap a four-game postseason losing streak, their first bowl win since beating Colorado 38-16 in the Fiesta Bowl after the 2001 season.
Oregon made it look easy against the Bulls (9-4), who boasted one of the nation's better defenses.
The Ducks won for the first time since losing quarterback Dennis Dixon to a knee injury in November, snapping a three-game losing streak that spoiled their national title hopes.
Roper, a redshirt freshman, started the scoring avalanche with a 14-yard TD strike to Jaison Williams and added a 15-yard scoring pass to Ed Dickson.
On the next play from scrimmage, Walter Thurmond stepped in front of a pass by South Florida's Matt Grothe and returned it 25 yards for another TD, giving the Ducks a 39-14 lead midway through the third.
Grothe had another interception on the ensuing possession, the first of two for Oregon's Jairus Byrd, setting up Roper's 8-yard TD pass to Stewart.