The Volunteers won on the road for the first time in four games and moved into a tie with South Carolina atop the Southeastern Conference Eastern Division. More importantly, the Vols (18-10, 9-5) strengthened their NCAA tournament resume with their fifth consecutive win against Florida (21-8, 8-6).
The Gators made it close, though. Florida trailed 59-43 midway through the second, but used a barrage of big shots to make it 75-72 with one minute left. But Scotty Hopson tipped Erving Walker's tying 3-point attempt, then Nick Calathes misfired on a baseline drive.
Smith hit 3 of 4 free throws in the final 17 seconds to seal it.
Calathes led the Gators with 20 points and seven assists. Walker added 16.