Shane Southwell added 16 points for the Wildcats (13-4, 3-1 Big 12), who rallied from a 62-56 deficit with just over 5 minutes to play to turn back the streaking Sooners.
Ryan Spangler had a career-high 21 points and 14 rebounds, and Buddy Hield scored 12 points for Oklahoma (13-4, 2-2), but it wasn’t enough to offset a lousy night by Cameron Clark.
The Big 12’s leading scorer, Clark was held to two points on 1-for-9 shooting. He was stripped of the ball with 24.5 seconds left and the Sooners trailing 67-64.
The turnover forced Oklahoma to foul, and Williams made both free throws. Je’lon Hornbeak missed a 3-pointer at the other end and the Sooners fouled Williams, and again he knocked down both foul shots to help seal the game.
Wesley Iwundu added 11 points for Kansas State while Williams and Will Spradling finished with 10 points apiece.
The Sooners, the highest scoring team in the Big 12, got the up-and-down game they wanted in the first half. The only problem was that Kansas State, which tends to struggle offensively but is the league’s best on defense, was knocking down shots from all over the court.
The Wildcats hit 3-pointers on five straight trips midway through the first half. Foster had the first three, thumping his chest on his way back to the bench after the last of them.
Kansas State eventually pushed its lead to 28-19 on Iwundu’s 3-pointer before the Sooners started to find some success in the paint. Isaiah Cousins’ driving layup started an 18-5 run over the next 7 minutes, capped by Hield’s basket for a 37-33 lead.
The Wildcats answered with a 3 by Southwell, and Spradling was fouled just before the halftime buzzer and made three free throws to give Kansas State a 39-38 lead.
Oklahoma slowly took control in the second half as the Wildcats cooled off. Spangler’s three-point play with 6½ minutes left gave the Sooners a 58-56 lead, and a breezy jumper by Cousins from just inside the 3-point arc extended the lead with about 5 minutes to play.
Once more, Kansas State clawed right back.
Big man Thomas Gipson stuck back a miss by Southwell for his first field goal with 2:59 left in the game to knot it 63-all. Foster then buried a 3-pointer from right in front of Kansas State coach Bruce Weber to give the Wildcats a 66-63 lead.
They managed to hold onto the lead through a tense closing stretch.