Tennessee (13-3, 4-0) improved to 4-0 in the SEC with the win over Florida (13-5, 2-2).
The Gators overcame an early nine-point lead by Tennessee in the second half, weathered the loss of Jennifer George to a shoulder injury before halftime and took a one-point lead, 70-69, with 26 seconds to play.
But Tennessee's Bashaara Graves hit one of two free throws to tie the game with 13 seconds left and Jaterra Bonds lost the handle on the Gators' last possession.
The Lady Vols didn't secure the game in overtime until Kamiko Williams hit one of two free throws and Florida's Christin Mercer missed both of hers.
Both teams will watch the game tape later and see missed chances, but the Lady Vols managed to lead Gainesville with the win.
Meighan Simmons led all scorers with 27 points, while Graves notched 17, Ariel Massengale added 12, and Isabelle Harrison chipped in with 10.
Bonds led Florida with 18 points, while Carlie Needles and January Miller added 11.
The Lady Vols next play at Auburn on Thursday at 9 p.m. Eastern.