ROSEMONT, Ill. -- Give the ball to Salim Stoudamire and get out of his way. That's what Arizona did last night.

Stoudamire made an off-balance jumper from the left side with 2.8 seconds left, sending Arizona to a pulsating 79-78 victory against Oklahoma State in the Chicago Region semifinals and within one win of the Final Four.

When John Lucas' last-ditch attempt went off the rim at the buzzer, the Wildcats had another memorable victory under coach Lute Olson.

Arizona (30-6) will meet top-seeded Illinois tomorrow for a trip to St. Louis. The Illini (34-1) defeated Wisconsin-Milwaukee, 77-63, earlier last night at Allstate Arena.

Stoudamire scored 10 of his 19 points in the final 4:35 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 made two NBA-range 3-pointers to get Arizona within 76-75.

After a defensive stop, Arizona's Channing Frye made 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 Oklahoma State its final lead at 78-77 with 18.8 seconds left.

After a timeout, Stoudamire waved his hand to clear out the floor and then maneuvered past Daniel Bobik and popped in a jumper from the left side, putting the Wildcats up, 79-78, with 2.8 seconds left.

"I knew when it came down to crunch time I was going to step up," Stoudamire said. "I practice that shot everyday. Coach is always on me about going hard, I guess it paid off."

Arizona had a foul to give, cutting the clock to 1.3 seconds, but the Cowboys still managed to get off a decent shot. But Lucas' attempt from the corner hit the rim, denying coach Eddie Sutton a second consecutive trip to the Final Four.

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

Saddled with two early fouls, Stoudamire played just 10 first-half minutes, but when the game seemed to be slipping away, he was there at the end.

Hassan Adams also finished with 19 points and had 10 rebounds for Arizona, and Frye added 15 points and 10 rebounds.

Graham, who had scored just 15 points total in his team's first two tournament games, was a different player last night, but it still wasn't enough.

JamesOn Curry and Graham connected on back-to-back 3-pointers and the Cowboys overcame an early seven-point, second-half deficit to lead, 52-51.

But the persistent Adams connected on his third 3-pointer and then followed up his own miss on the second try to put the Wildcats up, 59-56, a lead that went to five when Frye made a short jumper.

Graham hit two 3-pointers and Stephen Graham made a 3 to give the Cowboys a 69-65 lead.

Stoudamire drove for a basket and after a 3-pointer by Curry he answered with one from NBA range, cutting the Cowboys lead to 72-70 with 3:57 left.

Arizona shot 70 percent in the first half, making 16 of 23 shots and built an early 10-point lead.

But with Stoudamire off the floor earlier, the Cowboys took off on an 11-3 run, tying the score at 30-30 as Lucas and Ivan McFarlin hit back-to-back three-point plays and then taking a lead on two free throws by Graham.

Stoudamire, who had five 3-pointers and 28 points in second-round victory against UAB, came out firing.