Brandon Crump added a career-high 19 points for the Vols, who ended their five-game losing streak to the Gators and made another push toward returning to the NCAA tournament.
Florida, which beat Tennessee 77-64 in Gainesville last month, couldn't sweep the series this year.
The Gators led most of the game but gave up the lead for good with five minutes left. They got as close as 59-57 with two minutes to go, but did not get the lead the rest of the game.
Matt Bonner's basket in the lane with 38.8 seconds remaining were Florida's only points in the final minutes.
"I told the team we're going to have to win the game with defense, not offense,'' Tennessee coach Buzz Peterson said.
"It's called Smokey. We try to get after you. We gave it a name just because we take pride in it. We want to get stops on the defensive end.''
Peterson didn't divulge the details behind Smokey, which is the name of Tennessee's blue-tick hound mascot, but apparently it worked.
"It's tough to overcome when our three shooters, Brett Nelson, Anthony Roberson and Matt Walsh go a combined 3-for-22,'' Florida coach Billy Donovan said. "We have too much firepower to have scored just 59 points.''
Tennessee trailed by as many as eight in the second half, but tied it at 48 with 5:42 left on Crump's two free throws.
Bonner hit a jumper at the foul line to put Florida back in front, but Jon Higgins made a 3-pointer at the other end to give Tennessee the lead for good.
The Vols ran their lead to five, but Bonner hit a 3 with 2:17 to go to close the gap to two.
Justin Hamilton fouled Higgins shooting a 3 and made him miss, but Higgins made all three free throws to put Tennessee up 62-57 with 1:46 remaining.
Bonner scored Florida's final basket to cut the lead to 59-62. Tennessee then scored the final four points of the game, all on free throws.
The Gators had chances to score but they either missed the shot or turned the ball over.
The Gators came into the game shooting a league-best 77.4 percent on free throws in conference games, but made just 5-of-10 against Tennessee.
The Vols, meanwhile, were 17-of-21 from the foul line after going just 1-for-1 in the first half.
Tennessee tied the game three times in the first half but didn't lead until Crump's three-point play with 40.9 left put the Vols up 28-26. But the Gators regained the lead when Nelson hit a 3 with 7 seconds to go, and C.J. Watson missed a jumper at the halftime buzzer.
Florida started the second half strong. After the Vols went ahead by one, the Gators had a 9-0 run. Lee scored three straight baskets and Christian Drejer finished it with a 3 for a 43-35 lead with 14:59 remaining.
Florida looked like it was going to run away with the game at the beginning. The Gators made four of five 3-point attempts to open the game and led 14-5.
Tennessee slowly trimmed the lead, finally putting together a 12-2 run in which Slay scored eight straight points. Crump scored inside to tie it at 21 with 6:24 remaining before halftime.