Given an opportunity to pull off a major upset of No. 4 Kansas, in-state rival Kansas State simply self-destructed.

"That happens to us," coach Frank Martin said. "When you've got grown men playing for you, it makes our guys look like little kids in that moment."

Kansas State held national player of the year candidate Thomas Robinson to 10 points, and Jamar Samuels scored a season-high 20 for the Wildcats, but they couldn't hang tough down the stretch in Monday night's 59-53 loss that was filled with missed opportunities.

They briefly pulled ahead midway through the second half, and were within 55-51 when Rodney McGruder knocked down a jumper with 1:14 left. But they came up empty on their next three trips down the court, unable to take advantage of the Jayhawks' balky foul shooting.

Robinson made two free throws to put the Jayhawks up 57-51, and although McGruder hit another shot with 8.1 seconds left, Kansas State had run out of time.

Tyshawn Taylor had 20 points for Kansas (21-5, 11-2), and Jeff Withey added 18 points, 11 rebounds and nine blocks to help put his team alone in first place in the Big 12. In the process, the Jayhawks dealt the Wildcats their 36th loss in their last 39 meetings.

Samuels' big game could not overcome the youthful mistakes of the Wildcats (17-8, 6-7) — freshman guard Angel Rodriguez turned the ball over five times in the first half.

"I just wanted to beat them," Samuels said. "You've got a big-time team coming into your home, and it's a rivalry game, and you want to win."

McGruder finished with 12 points for Kansas State, while Will Spradling had 10.

The Jayhawks, who used a big first-half run en route to a 67-49 win in Lawrence last month, got off to another good start in the hostile environs of Bramlage Coliseum.

Taking advantage of some poor shooting by the Wildcats, Kansas got out in transition and slowly built a double-digit lead. Robinson's basket with 4:09 left before halftime made it 23-12, part of a stretch in which Kansas State went 7 minutes without scoring.

Thomas Gipson finally got on the board with 2:15 remaining, scoring the first points by anyone besides Samuels and McGruder in the first half. Samuels added two free throws in the closing minute to get the Wildcats within 28-18 at halftime.

It was the start of their only sustained run.

Spradling hit a jumper out of halftime, and Samuels knocked down two 3-pointers — a big confidence boost for someone who came into the game shooting 22.9 percent beyond the arc.

His second 3-pointer got Kansas State within 32-30, and a basket by Jordan Henriquez a couple minutes later tied the game. Gipson's free throw with 11:47 left gave the Wildcats a 37-36 lead, their first since it was 2-1 in the opening minutes of the game.

It didn't last long.

Taylor rattled in a 3-pointer from the top of the key as the shot clock hit zero to put Kansas back into the lead. He added another 3 moments later, and Withey grabbed an offensive board and managed to coax home a layup.

Kansas State struggled to find an answer after the Jayhawks switched to a zone defense known as the triangle-and-two, something Self has employed against the Wildcats before.

"They're made to get you to stand around," Martin said. "It got the mission accomplished. It got us to stand around, and they slowed us down."

Taylor added a circus-like layup to make it 47-37 with 6:29 left, forcing Martin to call a timeout. The Jayhawks kept pouring on the pressure, with Taylor answering a basket by Gipson with his own soaring dunk along the baseline.

Gipson lost his cool on the next trip down court. The big freshman stood his ground and drew a charge on Robinson, his fourth foul, but said something as the two stood up. He was hit with a technical foul, and Withey knocked down both free throws to restore a 10-point lead.

Kansas survived some tense moments down the stretch to win another game in Manhattan.

"We're going to have to keep fighting these battles to win the league," Taylor said. "We just have to keep battling and keep getting better, because we still have a couple of tough games."