OMAHA, Neb. (AP) — The messages were flying in the Kansas locker room at halftime.

Elijah Johnson told his team to stop second-guessing itself. Tyshawn Taylor reminded the Jayhawks that they'd been in trouble before. Coach Bill Self finally stood up and told his team that it would take sheer toughness to rally past Purdue.

"When things don't go well and you get behind and you play uphill the whole way, it takes some energy and it takes some toughness," said Self, whose team fell behind by double-digits early and still trailed by six at the break. "My message to the whole team was trust each other."

All those messages came through loud and clear.

Johnson finished with 18 points, including the go-ahead basket in the final minute, and No. 2 seed Kansas held off Robbie Hummel and the No. 10 seed Boilermakers 63-60 on Sunday night in a dramatic third-round game in the NCAA tournament.

"I felt it would come down to one possession no matter what," Johnson said, "the whole time."

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 finally fell away.

The Jayhawks leaped in jubilation. The Boilermakers sank in defeat.

"It stinks," Purdue coach Matt Painter said. "It stinks to lose."

Thomas Robinson fought through double-teams all night for 11 points and 13 rebounds, and the Jayhawks (29-6) got enough production from everyone else to erase a 10-point second-half deficit and reach the Midwest Regional semifinals in St. Louis.

Kansas will face No. 11 seed North Carolina State.

"What a great game. It wasn't the best played, but it was a grind-it-out, typical Big Ten game," Self said. "Hummel was unbelievable and we just hung in there."

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 finished with 10 points each for Purdue.

The Jayhawks' biggest lead all night was their final one. They overcame a ragged night from Robinson by getting 10 points from Taylor and 10 more from Travis Releford.

"That isn't a team loaded with just four or five guys," Painter said.

Purdue couldn't have gotten off to a much better start, and neither could Hummel, who hit three 3-pointers while making his first four shots. The senior forward, who has come back from two torn ACLs in his right knee, even followed his first miss with a basket to make 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."

Purdue extended the lead to 42-32 early in the second half, even after Kansas employed a zone defense to slow down Hummel. Johnson led the charge on offense, and the Boilermakers kept locking down Robinson in the post, frustrating the player of the year candidate to no end.

Kansas never went on its patented run, instead slowly clawing back into the game.

The Jayhawks trimmed the lead to 47-44 midway through the second half, but came up empty with four open shots on offense. They got within 52-49 minutes later only for Taylor to turn the ball over. And it was 52-51 with 5½ minutes left when Hummel drove for a layup high off the glass.

Kansas never led until Johnson hit a deep 3-pointer with just over 3 minutes left to make it 57-56. Terone Johnson answered with back-to-back baskets for Purdue to regain a 60-57 lead, but Taylor's alley-oop jam off a feed from Elijah Johnson made it a one-point game.

And set up a dramatic final flurry between Kansas and Purdue.

"We just kept grinding and grinding," Taylor said, "and we ended up making some big plays down the stretch."

NCAA TOURNAMENT

Third round

At Omaha, Neb.

CenturyLink Center

Sunday

Kansas 63, Purdue 60

PURDUE (22-13)

Hummel 9-13 3-5 26, Byrd 3-6 2-2 10, Marcius 0-2 0-0 0, T. Johnson 3-10 4-6 10, Jackson 2-11 1-2 5, A. Johnson 1-4 2-4 4, Smith 1-2 0-0 3, Lawson 0-0 0-0 0, Carroll 1-2 0-0 2. Totals 20-50 12-19 60.

KANSAS (29-6)

Robinson 2-12 7-11 11, Withey 1-3 2-2 4, Taylor 4-11 2-2 10, Johnson 7-14 1-1 18, Releford 4-7 2-4 10, Tharpe 1-3 0-0 3, Teahan 2-8 0-0 6, Wesley 0-0 1-3 1, Young 0-4 0-0 0. Totals 21-62 15-23 63.

Halftime — Purdue 36, Kansas 30. Three-point goals — Purdue 8-18 (Hummel 5-9, Byrd 2-5, Smith 1-2, A. Johnson 0-1, Jackson 0-1), Kansas 6-24 (Johnson 3-8, Teahan 2-7, Tharpe 1-3, Releford 0-2, Taylor 0-4). Rebounds_Purdue 36 (Hummel 9), Kansas 44 (Robinson 13). Assists — Purdue 11 (Jackson 5), Kansas 10 (Taylor 4). Total Fouls — Purdue 16, Kansas 18. Fouled Out —None.  A — 16,998.