The Volunteers (22-9, 10-6 Southeastern Conference) secured the Eastern Division's No. 3 seed and will play LSU in the first round of the league tournament next week in Atlanta.
Georgia (17-12, 8-8) has lost two straight and three of four to become the East's No. 5 seed. Sundiata Gaines scored 18 points to lead the Bulldogs, who have yet to learn their first-round opponent.
Chris Lofton, who began the game with a 20.8 average as the SEC's leading scorer, had just 14 points on 4-of-10 shooting, but the junior guard took control of the game with 5:33 remaining and Georgia leading by two.
With Levi Stukes guarding him tightly, Lofton hit a 25-foot 3-pointer in front of the Tennessee bench that gave the Vols a 55-54 lead.
Winners of six straight and nine of 11 against Georgia, the Vols had a 12-point lead twice in the first half, the second time coming on Smith's 3-pointer.
The Bulldogs were just 5-of-21 on 3-point attempts, but Tennessee, which finished the regular season with a school record 279 treys, went 11-of-26.
Ramar Smith had 13 for the Vols, and Brown finished with 13 for Georgia.