ROSEMONT, Ill. - Salim Stoudamire wanted the ball and he got it. He cleared out the floor with a wave of his hand and then hit the shot that moved Arizona within one win of the Final Four.

Stoudamire sank an off-balance jumper from the left side with 2.8 seconds left, sending Arizona to a thrilling 79-78 victory over Oklahoma State in the Chicago Regional semifinals Thursday night.

“I thrive on those situations. That’s what I live for,” Stoudamire said. “That’s why I play basketball. Bigtime players step up in bigtime situations, and I see myself as one of those players.”

Oklahoma got a last chance at victory but John Lucas, who has hit his share of big shots for the Cowboys, watched as his jumper from the corner went off the rim at the buzzer.

“When I let it go, I thought it was going in. When it hit the back of the rim, my heart just dropped. It’s just a real sad moment right now,” Lucas said.

Arizona (30-6) will meet top-seeded Illinois on Saturday for a trip to St. Louis. The Illini (35-1) defeated Wisconsin-Milwaukee 77-63 Thursday.

“Any team that comes into this Chicago region knows that if you’re going to get to St. Louis, it’s going to be by way of the University of Illinois. We’re happy to be in a situation where we get a chance to play,” Arizona coach Lute Olson said.

FREE VIDEO Down to the last shot March 25: Arizona coach Lute Olson, Wildcat story Salim Stoudamire, Oklahoma State star John Lucas and coach Eddie Sutton discuss Thursday night’s game.

Olson is now 3-0 against Oklahoma State coach Eddie Sutton, his fellow 700-victory club member, but this was their first meeting ever in the NCAA tournament.

Sutton told Olson after the game he thinks the Wildcats can beat Illinois. Later Sutton denied a report he was going to step down after the loss and turn over the program to his son, Sean, with the Cowboys losing so many key players.

“That’s why I would not retire next year. ... I don’t want to leave Sean in that position. We take some hits next year, I want to be the one who takes ’em,” Sutton said.

Stoudamire scored 10 of his 19 points in the final 4:35 of the game and the Wildcats shot 66 percent (31-of-47).

Scoreless in the second half until six minutes remained, Stoudamire drove for a basket and then hit two NBA-range 3-pointers to get Arizona within 76-75.

After a defensive stop, Arizona’s Channing Frye hit a short jumper, putting the Wildcats ahead 77-76 with a minute to go.

Joey Graham, who led Oklahoma State (26-7) with 26 points, then drove to the middle, lowered his shoulder and dropped in a short shot from the lane to give OSU its last lead at 78-77 with 18.8 seconds left.