The Volunteers (17-10, 9-7 Southeastern Conference) won for the fourth time in five games in Nashville against their instate rival, and they had the added bonus of handing Vanderbilt (10-17, 3-13) its ninth straight loss.
The Commodores looked like a much different team than the one that lost by 62 points at Kentucky on Wednesday night and led most of Saturday's game.
But Tennessee, which plays Mississippi on Thursday in the opening game of the SEC tournament in New Orleans, desperately needed a victory to improve its NCAA tournament hopes. The Vols got their edge with a 12-1 run in a very streaky game.
Vanderbilt turned a 29-27 halftime lead into a 43-33 edge with a 14-6 spurt. The Vols struggled to keep up as Slay, the SEC's leading scorer averaging 21.6 points per game, picked up his fourth foul with 13:51 left.
Crump, who had a game-high 11 rebounds, took up the slack with a quick four points and later started a stretch of seven-straight scoring possessions for the Vols. Slay added a pair of free throws and a basket during the run. A C.J. Watson steal and dunk with 4:49 to play gave the Vols a 56-55 lead, their first since 4-0.
Tennessee will play all of their SEC tourney games on 1pm EST. They will play Ole Miss in the first round game. If they win, they will move on to meet the Mississippi State Bulldogs for the second time in ten days.