McRae also had two steals and two blocked shots as Tennessee (17-10, 9-6 SEC) extended its winning streak to six games and handed the Gators (22-5, 12-3) their second loss in three starts.
Trae Golden and Jarnell Stokes both scored eight points for the Volunteers. Stokes had 14 of Tennessee's 40 rebounds.
Mike Rosario led Florida with 16 points and Patric Young added 15. The Gators, who had 29 rebounds, lead Alabama in the SEC by one game.
Florida cut Tennessee's lead to 54-58 with 2:03 to play in the game but scored only two field goals the rest of the way while the Vols went 5-for-4 from the free-throw line.