Osby went 6-of-8 from the field on his way to 17 points while Pledger put in 15 for the Sooners (15-7, 6-4 Big 12), who led wire-to-wire and snapped a 10-game skid against Kansas.
The Jayhawks (19-4, 7-3), meanwhile, dropped a third consecutive game for the first time since 2005 while going just 11-of-20 from the foul line.
Ben McLemore put in 15 points and Jeff Withey added 14 for Kansas.
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance
Reindeer recovered after escaping from Santa during lighting ceremony