Brittney Griner had 26 points and seven 67, on Sunday to snap the Lady Vols' 38-game home winning streak.
Odyssey Sims added 23 points and Jordan Madden scored 11 for the Lady Bears (6-0), who held Tennessee under 30 percent shooting and went 22-for-24 from the foul line.
Shekinna Stricklen scored 25 points to lead Tennessee (2-2) while Vicki Baugh added 17 and Taber Spani had 10.
The Lady Vols have lost two straight, also falling at Virginia in overtime last Sunday. Their 38-game home winning streak was the third-longest in team history.
Baylor, which held an opponent under 50 percent shooting for the 180th straight game, trailed 33-31 at halftime but took the lead for good when Sims' three-pointer made it 56-53 inside eight minutes.
Sims scored Baylor's final nine points from the free throw line in the last minute of the game.
Griner's seven blocks gave her 427 for her career. Oklahoma's Courtney Paris holds the Big 12 record at 446.
The Lady Bears took a 3-2 lead in the all-time series.