Whitney Hand added eight points for the Sooners (12-3, 2-0 Big 12), who trailed 20-15 at the break after shooing 6 for 31 from the field and committing 10 turnovers.
Brittany Chambers scored 11 points and Mariah White and Taelor Karr added nine each for the Wildcats (11-4, 1-1).
However, the Sooners made their first three shots after halftime and five of their first six, taking their first lead less than 5 minutes into the second half at 28-26.
While the Sooners struggled shooting, Kansas State wasn't much better. The Wildcats shot just 34 percent for the game and turned the ball over 19 times. Kansas State shot just 2 of 12 from the 3-point line.
Oklahoma, second in the nation in 3s made per game at 8.9, missed all nine of its attempts -- including six in the first half. It was the first game the Sooners didn't make a 3 since missing all eight against Texas A&M last March.
Oklahoma's scoring total was a season low as it shot just 32 percent for the game.
Sooners coach Sherri Coale won the United Nations NGO Positive Peace Award, which recognizes individuals, sports teams, entertainers throughout the country. She was presented with the award before the game Wednesday.