Updated

Tyshawn Taylor had 20 points in a virtuoso performance for No. 4 Kansas, which fended off a stiff test from Kansas State for a 59-53 victory Monday night that put the Jayhawks alone in first place in the Big 12.

Jeff Withey added 18 points and 11 rebounds in another impressive performance, helping make up for an off game by Thomas Robinson and allow the Jayhawks (21-5, 11-2) 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.

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, 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.

Taylor added a circus-like layup to make it 47-37 with 6:29 left, forcing Wildcats coach Frank 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.

Jayhawks coach Bill Self improved to 19-3 against the Wildcats. That mark includes 18 wins since he took over as the coach of Kansas.