OMAHA, Neb. — Kansas' Thomas Robinson knew there could be games like this in the NCAA tournament.
Sometimes it's just a matter of surviving.
The No. 2-seeded Jayhawks did, taking their first lead late and holding on to beat No. 10 seed Purdue 63-60 Sunday night and advance to the regional semifinals for the fifth time in six years.
"Something like that is stuff you have to face to win a championship," Robinson said. "Coach said there is going to be that ugly game. That was as ugly as I've seen."
Elijah Johnson scored 18 points, including the go-ahead basket in the final minute, to help Kansas overcome a monster shooting performance by Purdue's Robbie Hummel.
In the West Regional game, Florida defeated surprising Norfolk State 84-50 after blowing open the game with an early 25-0 run.
Kansas (29-6) heads to St. Louis to play North Carolina State in the Midwest Regional and Florida (25-10) travels to Phoenix to play Marquette in West Regional.
The Jayhawks' Robinson fought through double-teams all night for 11 points and 13 rebounds against Purdue, and they got enough production from everyone else to erase a 10-point second-half deficit.
Robinson, the Jayhawks' national player-of-the-year candidate, was just 2 for 12 and Tyshawn Taylor was 4 of 11.
"If Elijah didn't turn around," Robinson said, "we would have lost that game tonight."
Purdue was clinging to a 60-59 lead and had the ball and under a minute remaining when Lewis Jackson, the shot clock winding down, lost control at the top of the key. Johnson picked it up and went the other way for the go-ahead lay-in with 23.3 seconds left.
Hummel missed an open 3-pointer at the other end and Taylor scored a transition dunk for the Jayhawks with 2.5 seconds left, giving the roughly 15,000 fans who had made the three-hour drive from the Kansas campus reason to let out a roar for one of the first times all night.
After a timeout, Purdue sharpshooter Ryne Smith managed to get off a decent look at a long, potential tying 3-pointer. It hit off the backboard, clanked off the rim and fell away.
"It stinks," Purdue coach Matt Painter said. "It stinks to lose."
Hummel finished with 26 points and nine rebounds for the Boilermakers (22-13), who were trying to reach the round of 16 for the third time in four years. D.J. Byrd and Terone Johnson had 10 points each for Purdue.
The Jayhawks' biggest lead all night was their final one. They overcame a rough night by Robinson by getting 10 points from Taylor and 10 more from Travis Releford.
"Coach said that for us to win this game, we have to make them play bad in the first half. We didn't," Taylor said. "We made eight turnovers, they missed 10 shots in the first half and got six offensive rebounds. So we weren't doing anything to stop them. We kept grinding. When we needed the stops, we knuckled down and got them."
Purdue couldn't have gotten off to a much better start.
Neither could Hummel.
The senior forward hit his first four shots, three of them from beyond the arc, and followed up his first miss with another basket with 11:46 to go in the first half that made it 19-8.
He proved too quick for Robinson to guard and too strong for Kevin Young as the Jayhawks kept searching for anybody who could put a body on him — they even tried seldom-used Justin Wesley.
The miserable start by Kansas was enough for Self to scream at his team during one defensive trip down floor, "You told me you were ready!"
Hardly seemed to be the case.
Kansas opened the game by missing 15 of its first 17 shots and all seven of its 3-point tries, compounding lousy offense by getting into foul trouble. Taylor, Young and Releford all sat stretches in the first half after picking up two early fouls.
The Jayhawks finally trimmed the lead to 31-30 with under 3 minutes left in the first half, but Lewis Jackson got inside for a basket, and Hummel managed to swish a closely guarded 3 from about 30 feet as the shot clock wound down to make it 36-30 at the break.
Hummel had 22 points on 7-of-8 shooting in the first half, while the Jayhawks' trio of stars — Robinson, Taylor and Johnson — managed 12 points on a combined 4-for-18.
"I wanted to come out and be aggressive, especially the first half. It seemed like everything I was taking was going in," Hummel said. "It was a crazy feeling you have as a player."
Earlier in the day, Florida put an end to the feel-good story that was Norfolk State.
Any hope Norfolk State had of matching the upset it pulled against Missouri on Friday vanished as the Gators went on a 25-0 run in the first half.
The Gators had a business-as-usual air about them after dispatching the Spartans (26-10). After all, Florida is 17-2 in NCAA tournament games since 2005-06. Combined with their 71-45 win over Virginia on Friday, the Gators left Omaha with two wins by a total margin of 60 points.
Not too shabby for a No. 7 seed.
"There are certain guys who want this kind of stage," Florida coach Billy Donovan said. "In this tournament you have to have players who play fearlessly on both ends of the floor and are not worried about making mistakes and are competitive and are driven to want to be great."
AP Sports Writer Dave Skretta contributed to this report.