Kansas State built an early lead by turning over Florida twice in the opening minutes, and the Gators responded with a 9-2 surge in which they twice scored off turnovers in transition.
Kansas State eventually settled down on offense.
McGruder's basket with just under 5 minutes left made it 26-19, and after the Gators' Michael Frazier curled in a 3-pointer for his only basket, Kansas State rattled off seven more points that helped it take a 33-23 lead into the break.
The lead was built on the Wildcats out-defending the nation's No. 1 defense.
"Our guards made some very poor plays in the first half in terms of our ball movement," Donovan said. "We were very insistent on driving the ball and taking runners and floaters in the lane. ... We had guys open all over the place. All we had to do was make the extra pass."
Florida started to make that extra pass early in the second half.
The Gators scored on their first six trips down the floor and put together a 12-3 run that allowed them to wipe out almost the entire deficit. Boynton's 3 with 13:10 left drew them even at 41-all, the closest they'd been since leading 19-17 midway through the first half.
"I just said, 'We've been here before,'" Weber said. "You get a point where the other team comes at you and do you lay down or do you step up?"
The Wildcats kept stepping up.
Rosario's first basket, a 3-pointer with 10:42 left, was matched by McGruder's jumper. A bucket by Wilbekin was matched by a 3-pointer from Kansas State's Martavious Irving, and slowly the Wildcats extended the lead back to 57-47 with 5:20 left.
Things were going so well for Kansas State that Henriquez, who had been 2 for 19 from the foul line, stepped up and calmly knocked down four straight free throws.
"When I hit those four in a row, it felt good," he said. "I felt good."
It was a feel-good night all-around for the Wildcats.
They wound up shooting 41.7 percent from the field against a team that had been holding opponents to 49.6 points per game. The Wildcats also ended up with a 36-27 advantage on the glass and committed just 10 turnovers against the Gators' intense man-to-man defense.
"This was a great win for our team, great win for our staff, a great win for our league," Weber said. "This was a great win for us."