KANSAS CITY, Mo. -- Oklahoma State had a good game plan against No. 2 Kansas. If not for all that foul trouble, it might have been good enough to pull off a major upset.

Mario Little's three-point play broke a tie with 71 seconds to go and the depleted Cowboys missed a desperation heave at the buzzer, allowing the Jayhawks to escape with a 63-62 victory Thursday in the quarterfinals of the Big 12 tournament.

Oklahoma State, routed by Kansas last month, led by as many as eight and did a good job of keeping Marcus and Markieff Morris from operating down low, forcing the 14-point favorites to put up an uncharacteristic 25 3-pointers. They made only five and were in trouble the entire game.

"We usually shoot about 30 percent of our shots as 3s," Kansas coach Bill Self said. "When we're playing well, it's more like 10-15 percent. That's as tight as anybody has played us all year. They went zone. The looks we were going to get were guys open on the perimeter. When the bigs went out, they probably condensed it more and we didn't make them pay."

Marcus Morris, the Big 12 player of the year, had 16 points and 11 rebounds but was shut down for most of the second half until he hit a key 3-pointer for the Jayhawks (30-2).

Keiton Page had 23 points and Jean-Paul Olukemi scored 17 for Oklahoma State (19-13). The Cowboys were 18 for 21 from the foul line but had three of their big men foul out. Kansas was only 12 of 21 from the line.

Marcus Morris hadn't made a field goal since the 8:26 mark of the first half when he drilled a 3 that put the Jayhawks ahead 58-54 with 4:07 left.

"The Morris 3, from about 35 feet, was the biggest shot of the game," Oklahoma State coach Travis Ford said. "That was huge. That was bigger than the one we missed at the end."

About 30 seconds after Marcus connected, Markieff fouled out and Olukemi made both foul shots.

With 2:55 to go, Marshall Moses, Oklahoma State's top scorer all season, became the third Cowboys player to go to the bench with his fifth foul. But Page, finding an open space down the middle, hit a floater that made it 60-58.

With 1:28 left, Page tied it at 60 with two more fouls shots, and that's when Little worked inside for a bucket, got fouled and made the free throw for a 63-60 Kansas lead. Olukemi cut the deficit to 63-62 with a 10-foot jumper.

"We were doing everything, all the little things, to try to come up with a win tonight, all the loose rebounds, helping everybody on rotation rebounding," Page said. "Those are the types of things you have to do to win a game against a team like Kansas."

The Jayhawks gave up the ball on a shot-clock violation with 20 seconds left, but Olukemi's desperation heave missed at the buzzer.

"I was praying a little bit at the end," Self said. "We couldn't keep them off the free throw line. I was more concerned about us fouling than them making a shot."

Markieff Morris had 10 points and Brady Morningstar 11 for Kansas, which shot only 36 percent -- far below its nation-leading season average of 51.8 percent.

The Jayhawks, who beat Oklahoma State 92-65 last month, struggled to regain the lead and Little brought a roar from the partisan Kansas crowd with a 3 that finally tied it at 47-all. Then Tyshawn Taylor, with an assist from Thomas Robinson, got a layup for a 51-50 lead.

"Rio [Little] is our off-the-bench spark," Marcus Morris said. "When he came in with about 1½ minutes to go and missed a couple of middle shots, I told him to just stay aggressive because they were small and that gave me a better chance of getting it off of the rebounds."

But the Jayhawks started running into foul trouble of their own. Markieff Morris got his fourth foul with 10:32 to go and 3 minutes later point guard Elijah Johnson picked up his third and fourth fouls within seconds of each other.

In spite of drawing two technical fouls, the Cowboys led by as many as eight in the first half and took a 41-35 lead into intermission. Olukemi was whistled for a technical early in the first half after a dunk and Markel Brown drew a "T" for saying something to a Kansas player when the Cowboys took possession after a furious struggle for a rebound under the Kansas basket.

But in each case, Tyrel Reed, Kansas' best free throw shooter, was able to convert only one foul shot.