MANHATTAN (AP) -- Tyshawn Taylor heard the Kansas State fans razzing him during pre-game warmups. The senior guard for No. 4 Kansas understands that the confidence he exudes rubs some the wrong way.

Here's the thing, though: He backs up the bravado when the game is on the line.

Taylor scored 10 of his 20 points during a key stretch of the second half Monday night, allowing the Jayhawks to survive a stiff test from the Wildcats in a 59-53 victory.

And it was Taylor who had the last word.

"They had a chance to talk to me while I was warming up," he said of the fans in Bramlage Coliseum. "I felt like I had my chance to talk to them a little bit after the game."

Taylor popped the front of his jersey in the closing minutes, no doubt irking the purple-clad fans who had worked themselves into a frenzy during the Wildcats' second-half charge.

The one that Taylor seemed to answer all by himself.

"Tyshawn has been unbelievable in conference play," Kansas coach Bill Self said. "Arguably as good a player as there is in the league in conference play."

Jeff Withey added 18 points 11 rebounds and nine blocks in another impressive performance, helping make up for an off game by Thomas Robinson and allow the Jayhawks (21-5, 11-2 Big 12) to win for the 36th time in their last 39 games against the Interstate 70 rival.

Kansas moved one-half game ahead of No. 3 Missouri (23-2, 10-2), which plays Oklahoma State on Wednesday night, in the race for the regular-season conference championship.

Jamar Samuels had a season-high 20 points and 12 rebounds for the Wildcats (17-8, 6-7), who missed out on a golden opportunity to tack a signature win on its NCAA tournament resume.

The Wildcats were not without their chances.

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 in the game. But they came up empty on their next three trips down the court, unable to take advantage of the Jayhawks' balky foul shooting.

"This loss hurt," Samuels said.

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

"When you've got grown men playing for you, it makes our guys look like little kids," Kansas State coach Frank Martin said. "We have to prepare our guys to handle those situations."

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. Robinson's basket made it 23-12 with 4:09 left before halftime, part of a stretch in which Kansas State went 7 minutes without scoring.

Thomas Gipson finally got on the board with 2:15 remaining, the first points by anyone besides Samuels and McGruder for Kansas State. Samuels added two free throws in the final 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.

"He always makes 3s against us," Self said.

Samuels' 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 as the Jayhawks stretched it open.

Kansas State struggled to find an answer after the Jayhawks switched to a zone defense.

"Those junk defenses -- and I say that in a nice way, not a negative way -- they're made to get you to stand around," Martin said. "They got the mission accomplished."

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."