The Volunteers (2-2) had held a 23-7 lead at halftime. But the Blazers (1-3) staged their second major comeback in two weeks as David Isabelle found Frantrell Forrest on a 27-yard touchdown strike and ran for 6 yards for another score and Bryan Ellis hit Jeffery Anderson on two 2-point conversions.
Daniel Lincoln kicked a 40-yard field goal for Tennessee to open the first overtime, and UAB's Josh Zahn, who missed field goals from 30, 35, 41 and 49 in regulation, connected on a 35-yard field goal to answer.
Ellis hit Pat Shed on a 14-yard pass to pick up a first down in the second overtime but his 7-yard pass to Patrick Hearn came up 4 yards short of the end zone, and Zahn scored on a 21-yard field goal to put UAB up 29-26 before the Vols' final touchdown.
The Blazers dominated the game in nearly every category. They picked up 544 yards compared to the Vols' 287 yards, had eight more first downs and converted seven more third down attempts.
Tennessee's defense couldn't stop UAB, who used Isabelle, the backup quarterback, to chip away yards with his runs and Ellis, the starter, to convert third-and-long situations.
Ellis completed 29 of 55 for 373 yards, a touchdown and an interception. Isabelle ran 16 times for 73 yards and completed 4 of 5 for 56 yards and a touchdown.
Still, the Vols seemed to be in control in the first half. The Vols went for it on fourth-and-1 at the UAB 15 on its first drive and got two yards on a quarterback sneak by Simms, who threw a 13-yard touchdown pass to Moore on the next play.
UAB had just tied the game at 7 with a 52-yard touchdown pass from Bryan Ellis to Mike Jones with 2:34 in the first quarter, but Simms answered with a 72-yard touchdown to Zach Rogers on the next play. It was Tennessee's longest play since an 87-yard touchdown run by LaMarcus Coker against Vanderbilt in 2006.
With 1:55 before halftime, Chad Cunningham backed up UAB with a 54-yard punt to the Blazers 5, and Prentiss Wagner picked off Bryan Ellis on the next play and returned it 9 yards for a touchdown.
adidas Men's Tennessee Volunteers Sideline Coaches Tennessee Orange PoloPrice: $38.93 Shop
A UCLA football player was suspended indefinitely Friday after he was arrested on suspicion of rape.
The tougher tests await down the road for No. 3 Baylor Bears, but coach Art Briles has seen enough of his Bears to know this is his best team.
A decision has been made that Randy Edsall will not be the football coach at Maryland next season, and discussions are taking place about how and when to separate, a source said Thursday night.
Florida State running back Mario Pender has been released from the hospital but could be given a medical redshirt if he cannot return to the field this season.
The University of Wisconsin agreed to a 10-year deal with Under Armour on Friday worth a total of $96 million in cash and the retail value of products received.
Linebacker Myles Jack, who suffered a season-ending knee injury, said Thursday he decided to leave UCLA and enter the 2016 NFL draft because he wants to be compensated for his skills.