Pierre Jackson scored 17 points and Isaiah Austin and A.J. Walton each added 11 for the Bears (5-2). Brady Heslip and Cory Jefferson each added 10 points and Baylor beat the Wildcats for the first time in eight tries.
Baylor shot just 41 percent for the game but held Kentucky (4-3) to 21-of-71 from the floor.
Archie Goodwin scored 17 points for Kentucky before fouling out with 1:44 remaining in the game. Alex Poythress added 13 and Nerlens Noel eight for the Wildcats.
After trailing for the first 15 minutes Baylor took its first lead at 20-19 on Jackson's 3-pointer and stayed close before closing the half with a 12-2 run for a 34-29 lead. The Bears kept the Wildcats at bay with a zone defense that forced Kentucky into 16 turnovers.