The high-scoring guard had 23 points, but a big chunk came in the final minutes, when the Sooners (19-3, 7-3) were desperately trying to rally against a team that wouldn't budge an inch.
It was Kansas State's first victory against a No. 1 team since topping Kansas on Feb. 11, 2011, and just the fifth time the program has knocked off the nation's best team.
Ryan Spangler had 14 points and 10 rebounds for the Sooners, while Isaiah Cousins added 16 points. But the senior guard also fouled out with about a minute left when he committed a personal foul — his fourth — and then kicked the ball into the stands for a technical.
It was that kind of game for Oklahoma.
Hield was just 7 of 16 from the floor, and didn't attempt a free throw until there was about seven minutes left. Jordan Woodard went 0 for 5 and failed to score, and forwards Dante Buford and Khadeem Lattin were plagued by foul trouble.
The start of the game hardly provided any indication of the result.
Kansas State started in about the worst shape possible, turning the ball over four times without getting up a shot. And when it finally did, it was an air ball from 18 feet.
Oklahoma took advantage by scoring the game's first nine points, but was unable to deliver a knockout blow, and eventually Kansas State started fighting back.
Wade was the instigator, hitting a couple of 3-pointers and scoring 10 first-half points. But everybody else got into the act, too: Edwards converted a three-point play just before halftime, and a thunderous dunk by Iwundu a moment later gave Kansas State a 38-32 advantage.
By that point, Hield was so frustrated that he was barking at officials for fouls. The senior guard, averaging 25.8 points, was held to just six on 2-for-7 shooting in the first half.
Kansas State got off to a similarly poor start in the second half, turning it over twice and missing four of its first five shots, only to find its rhythm again. The hustling Wildcats tracked down every loose ball, and slowly turned a 45-41 deficit into a 58-50 lead.
Hield and the Wildcats then began matching each other blow for blow, with the plucky underdogs maintaining their cushion even when the talented guard began getting to the rim for easy layups.
Iwundu and Wade were there for big buckets down the stretch, and a team missing point guard Kamau Stokes because of an injury held its poise until the final buzzer.
Oklahoma: Lattin finished with six points and two rebounds. ... Hield finished 0-4 in his career at Kansas State. ... The Sooners have not won at Kansas State since 2012.
Kansas State: Freshman G Barry Brown started for the first time in place of Edwards, and Johnson started in place of Wade. ... The Wildcats shot 53 percent from the field.
Oklahoma plays Texas on Monday night.
Kansas State plays No. 15 Baylor on Wednesday night.