Beasley's bucket capped a monster performance for the freshman phenom, who outplayed his lofty expectations.
The forward finished with 32 points and 11 boards in what turned out to be a classic showdown between two of the country's top freshmen.
Oklahoma forward Blake Griffin added 27 points and 14 board of his own. His steal and dunk with 24 seconds left in the game knotted the score at 82-all.
Kansas State (11-4, 1-0) called a timeout with 13.2 seconds left.
Freshmen point guard dribbled at the top of the key until an opening appeared. He finally drove and found an open Beasley.
Griffin attempted to draw a charge, but to no avail. Austin Johnson's half-court heave bounced off the backboard and rim.
"Coach told us to stay down because they were going to get inside because that was all they needed," Griffin said. "I tried to slide over to take a charge. Give them credit, they made a play when it counted."
The final bucket was fitting for a back-and-forth game that saw 17 ties and 20 lead changes.
However, Kansas State didn't trail the final 5:27 after Blake Young nailed a 3-pointer to give his team a 72-69 lead.
That lead was pushed to 82-78 at the 1:08 mark on a trey from Clent Stewart, a Tulsa Union product.
Griffin sank two free throws 20 seconds later, then electrified the crowd with his steal and game-tying dunk.
Another freshman, Bill Walker, fought off foul trouble to spark the Wildcats early in the second half with consecutive 3-pointers. He finished with 22 points.
Kansas State was 8-of-17 from beyond the arc and shot 56.4 percent overall.
The Sooners (12-4, 0-1) were almost as good as they shot 52.8 percent.
But it wasn't enough to overcome the Wildcats, who moved to 1-0 in conference play and await visiting Texas A&M next Saturday.
The Sooners don't have that luxury. They'll board a plane Sunday for Lawrence, Kan., to take on the No. 2 Jayhawks Monday night.