Guard Cade Davis keyed the rally with his 21-point, seven-rebound performance which featured 8-of-9 shooting from the field.
Because of that, Kansas State virtually controlled the game from the opening tipoff, jumping out to an early 9-4 lead.
But the Sooners captured their only leads when they stormed back on a 7-0 run to go up 11-9 and followed the ensuing Wildcat bucket with one of their own to make it 13-11.
After the Wildcats regained the lead at 14-13 off a 3-pointer by guard Will Spradling, they never trailed again, carrying a 39-24 margin into intermission.
They led by as much as 19 on two different occasions in the second half.
Kansas State guard Rodney McGruder was the only other Wildcat in double figures with 20 points.
The Sooners dropped to 12-14 overall and just 4-8 in Big 12 play, while the Wildcats improve to 18-9 overall and 6-6 in the conference.