Rodriguez dished off 10 assists while Southwell finished with 18 points for the Wildcats (20-5, 9-3 Big 12), who shook off a Monday loss to intrastate rival Kansas.
Jordan Henriquez provided 10 points to go with 10 rebounds and Rodney McGruder scored 10 points for KSU.
The Bears (16-9, 7-5) got 14 points from A.J. Walton and 13 from Isaiah Austin.
Brady Heslip canned four 3-pointers en route to 12 points for Baylor which had won two straight coming into the game.