Russell Robinson made 14 of 15 free throws and scored 22 points for Kansas (23-1, 8-1 Big 12). Sherron Collins added 17 points for the Jayhawks, who scored 100 points for the second time this season, but also gave up a season-high 90.
Curtis Jerrells scored 30 points for Baylor (18-4, 5-3), which has lost three of its last four games.
LaceDarius Dunn had 23 points for the Bears, and Mamadou Diene had 10 rebounds and three blocked shots.
The Jayhawks led by just three points at halftime.