The Sooners (15-7, 6-4 Big 12) snapped a 10-game losing streak in the series and took down a top 5 opponent for the first time since beating No. 4 Texas on Jan. 28, 2006.
Freshman Je'lon Hornbeak went 4 for 6 at the free throw line in the final minute, just enough to keep the Jayhawks (19-4, 7-3) at bay. Cameron Clark hit two free throws to finish it off, and fans stormed the court after Buddy Hield came up with a steal and then dunked as the final buzzer sounded.
Kansas had the nation's longest winning streak at 18 games before losing three straight for the first time since February 2005.
Ben McLemore led Kansas with 15 points and Jeff Withey had 14 points, six rebounds and the one block he needed to tie Greg Ostertag's school record with the 258th of his career. The Jayhawks outscored Oklahoma 32-16 in the paint, but missed seven of their first 12 free throws to stall their attempts at a comeback.
Oklahoma had a 23-11 advantage in bench scoring, led by Clark's 10 points, to snap its own two-game skid.
McLemore drilled a 3-pointer from the right corner to start a string of eight straight Jayhawk points, cutting the deficit to 57-56 on Elijah Johnson's runner with 4:58 remaining before Amath M'Baye snapped a 4-minute drought for Oklahoma by hitting a 3-pointer.
Travis Releford had a chance to tie it at 60 before missing the second of two free throws with 4:12 to play, and Pledger connected on a 3-pointer from the right wing at the opposite end to give Oklahoma a smidgen of breathing room. Hornbeak then answered Withey's two-handed slam with a 3-pointer, and the Jayhawks were forced to foul when Johnson came up empty on a drive to the hoop.
Hornbeak hit one of two free throws for a 67-61 lead with 57.7 seconds left, then split another pair after Johnson hit a 3. McLemore's tip-in of a miss by Naadir Tharpe got Kansas within 68-66 with 15.7 seconds left.
Hornbeak then went 2 for 2 at the line when it counted the most.
The Jayhawks, who made just three baskets and scored 13 points in the first half of a loss at last-place TCU on Wednesday, surpassed that scoring total in just over 5 minutes as both teams got out to a crisp start. The problem for Kansas was at the other end, with the Sooners hitting 15 of their first 25 shots and leading by as many as eight points in the final minute of the first half.
Tharpe then earned a defensive 5-second call against Isaiah Cousins and had two baskets to get the Jayhawks within 38-34 at halftime. Kansas got as close as one before Osby's third-chance basket started a string of eight straight Sooner points to restore the lead to 55-46 with 10 minutes left.