The Jayhawks began their Big 12 Conference season with a road win that was in doubt until the closing minutes.
Oklahoma closed within 85-81 on a free throw by Cameron Clark with 1:55 to play, but Clark then missed a foul shot and the Sooners' Buddy Hield misfired on a 3-point attempt that would have reduced their deficit to a single point.
Tharpe then converted his foul shot to increase the Kansas lead to six and Oklahoma managed only two more points the rest of the way.
Kansas won its conference opener for the 23rd straight year with Wayne Selden, Jr. making five 3-pointers and scoring 24 points to lead the way. Kansas is 10-4 for the campaign.
Perry Ellis added 22 points and 11 rebounds for the Jayhawks and Tharpe had 17.
Clark hit 10-of-18 from the field and paced the Sooners (12-3, 1-1 Big 12) with 32 points.
Dennis Rodman pledges to end trips to North Korea
Interpol investigating stolen passports on missing flight