Quinn went 20-of-33 and had no interceptions as the Fighting Irish rose to 6-2 after their fourth win in five games.
Anthony Fasano had four catches for 78 yards and a touchdown; Maurice Stovall had one touchdown reception; Darius Walker gained 62 yards rushing on 15 attempts; and Jeff Samardzija had seven receptions for 127 yards and one score for Notre Dame.
Volunteers quarterback Erik Ainge was 13-of-32 passing for 187 yards, one touchdown and two costly interceptions; running back Arian Foster rushed for 125 yards on 28 attempts and one score; and wide receiver Bret Smith had two receptions for 21 yards and one touchdown.
Tennessee has lost four straight.
Celebrity Families of 2014 [PHOTOS]