The Vols (3-3, 1-2) forced three turnovers from Auburn's lackluster offense, intercepting Jarrett Stidham twice and getting a strip sack that resulted in touchdown by Alontae Taylor.
The Tigers (4-3, 1-3) are off to their worst SEC start since also going 1-3 in 2015.
Stidham's first pick led to a 42-yard touchdown pass from Guarantano to Ty Chandler that tied the game at 10 in the second quarter.
Guarantano got rolling from there. The sophomore spread the ball around, completing passes to eight different Volunteers, six of which finished with a double-digit average.
"I think (Guarantano) did a really good job today of him having an effect on his teammates," Tennessee coach Jeremy Pruitt said. "We had some guys today that I think played their best football."
Jauan Jennings capped a 12-play, 86-yard drive in the third quarter with a 25-yard touchdown catch to give Tennessee its first lead at 20-17 late in the third quarter.
Two plays later, Stidham was sacked and fumbled at his own 15. After several failed attempts to secure the loose ball, Taylor recovered in the end zone.
Stidham, who finished 28-of-45 passing for 322 yards and two touchdowns to go with his three turnovers, returned on the next drive to echoing boos inside Jordan-Hare Stadium.
"I'm very disappointed in our performance," Auburn coach Gus Malzahn said. "I'm disappointed for our players, I'm disappointed for our fans. I'm not happy."
Auburn scored with under a minute remaining on a Stidham TD pass to Seth Williams, but was unable to recover the onside kick attempt.
The Vols' offense entered the game ranked No. 94 nationally in third-down conversions, but Guarantano dissected the Tigers' secondary on those downs with 11-of-14 passing for 188 yards and a score. The Vols converted 10 of 19 tries on third down.
Tennessee: Pruitt got his first victory in the SEC and suddenly Tennessee can at least hope for a bowl bid in its first season under the former Alabama defensive coordinator.
Auburn: The Tigers started the season with playoff hopes, but they have regressed and can expect to be unranked on Sunday.
AUBURN STARTERS OUT
Tigers running back JaTarvious Whitlow (12 carries, 42 yards) was injured while trying to recover Stidham's fumble and did not re-enter the game. Safety Jeremiah Dinson was ejected for targeting on Jennings' touchdown and will miss the first half of next week's game at Ole Miss.
Tennessee: Pruitt's team hosts No. 1 Alabama next Saturday inside Neyland Stadium.
Auburn: The Tigers travel to Oxford, Miss., to face Ole Miss before their open week.