Walker led the Gators with 16 points and Kenny Boynton and Vernon Macklin each added 12. Alex Tyus chipped in 10 for Florida (20-5, 9-2 Southeastern Conference), which has won four straight and seven of eight.
Tennessee got 22 points from Scotty Hopson and 11 from Brian Williams. The Volunteers (15-10, 5-5) lost their third consecutive game and second in a row since coach Bruce Pearl returned from an eight-game SEC suspension for lying to NCAA investigators about a secondary violation.
The win also kept the Gators in control of the SEC East. Florida began the day with a 2½-game lead over four teams tied for second place.
Macklin went to the bench after picking up his third foul with 18:22 to play and Florida trailing 37-31. The Gators hung tough without his inside presence, though, trimming Tennessee’s advantage to 40-38 on a 3-pointer by Erik Murphy at the 12:19 mark.
The Volunteers’ lead was 43-38 when Macklin returned with 10:53 left and his dunk off a steal with 8:26 to play gave Florida a 48-47 edge.
Melvin Goins hit a jumper to tie it at 49 and Josh Bone’s 3 put the Volunteers back in front 52-49 with 6:25 left. Macklin’s hook in the lane tied it again at 53-all and a steal and dunk by Tyus put the Gators back up 55-53 with 3:49 remaining.
The Gators were leading 57-55 when Macklin was whistled for a blocking foul on Cameron Tatum’s layup attempt. Tatum hit one of two free throws with 2:29 left to cut the lead to a point.
Walker hit a pair at the line to make it 59-56 and Williams cut it to one again with a running hook. The Gators turned it over with 1:25 left and Tatum got a putback underneath to put Tennessee back up 60-59 with 46.8 seconds remaining.
Tyus was fouled by Williams going up for a dunk with 30.7 seconds left but missed the free throws. Tatum returned the favor, though, missing the front end of a one-and-one to set up the Gators’ final possession and Walker’s game-winner.
Tennessee led 35-29 at halftime, thanks to a combination of some strong shooting and Florida turnovers.
The Volunteers shot 53 percent in the opening 20 minutes, including 45 percent (5 of 11) from 3-point range. Hopson had a team-high 15 points for Tennessee, with Williams chipping in eight.
The Gators moved the ball well at times on offense in the first half, shooting 45 percent from the field. They also shot well (45 percent) and got 10 first-half points from Boynton. But their 10 turnovers, including nine Tennessee steals, kept them from getting into a true rhythm. The Volunteers scored 20 points in the paint and 13 off Gators turnovers.
Florida took a 17-13 lead on a 3-pointer by Scottie Wilbekin with 11:34 to play in the half. But Tennessee responded with a 10-0 spurt to make it 23-17 with 8:47 left.
Williams limped off briefly during the run with what looked like a left ankle injury. He went to the bench briefly and returned.
Leading 28-23, Tennessee had another scary moment with 2:42 left when Goins went up for a layup, missed the shot, and hit the back of his head when he landed.
But he was able to jog off the floor and, like Williams, was able to return after being checked out by team trainers.