J.P. Prince scored a game-high 23 points for the Volunteers (11-1), who have won six straight.
The Musketeers (8-3) led most of the second half and were up 73-69 with 4:17 remaining when Tennessee went into overdrive. Tyler Smith blocked a shot and Ramar Smith raced for a dunk that pulled Tennessee within 73-72. Tyler Smith then came up with a steal and dashed in with a layup that put the Volunteers in front with 2:18 left.
Ramar Smith followed with another steal and Tyler Smith's put-back made it 76-73. Wayne Chism's basket put Tennessee up by five with 49 seconds left.
A pair of Drew Lavender free throws ended the Volunteers' 9-0 run and made it 78-75, but Tyler Smith hit two free throws and Tennessee went on to the win.
Chism and Tyler Smith each finished with 12 points for the Volunteers, while Ramar Smith and Chris Lofton contributed nine apiece.