The Volunteers had a chance to improve on their 60-59 lead when Cameron Tatum went to the free-throw line with 26 seconds left, but he missed the front end of a 1-and-1 and Alex Tyus rebounded for Florida.
Walker was fed the ball at the other end and he drove the lane for a score, giving the Gators the lead.
Melvin Goins missed a desperation 3-point try for the Vols as time ran out.
Walker ended with 16 points and Kenny Boynton and Vernon Macklin chipped in with 12 apiece for the Gators (20-5, 9-2 SEC), who won for the seventh time in eight games and swept the season's series from Tennessee.
The Volunteers (15-10, 5-5) got 22 points from Scotty Hopson.
18-year-old elf alleges mall Santa pinched her buttocks on the job
Exploding whale video goes viral on Internet