Tharpe also dished off six assists for the Jayhawks (13-4, 4-0 Big 12), who blew a 19-point lead but managed to hang on for a fourth straight win against a ranked conference opponent.
Joel Embiid supplied 13 points, 11 rebounds and a career-high eight blocks, picking up the slack for freshman Andrew Wiggins, who was held to just three points.
The Cowboys (15-3, 3-2) got 23 points from Phil Forte, who drained 7-of-10 3-point attempts.
Marcus Smart ended with 16 points, 10 rebounds and nine assists. Markel Brown added 15 points for OSU.