NO. 5 KANSAS 59, KANSAS STATE 53: Tyshawn Taylor had 12 of his game-high 20 points in the second half — including consecutive 3-pointers during a key stretch late — as fifth-ranked Kansas held off host Kansas State.

Jeff Withey finished with 18 points, 11 rebounds and nine blocks for the Jayhawks (21-5, 11-2 Big 12), who swept the season series against the rival Wildcats for the third time in the last four years.

With the win, Kansas took a half-game lead over No. 3 Missouri in the Big 12 Conference standings with five to play. The Wildcats (17-8, 6-7 Big 12), meanwhile, fell into sixth place and will have plenty of work to do if they hope to advance to a third straight NCAA Tournament.

Kansas State took a 37-36 lead — its first of the second half — on Thomas Gipson’s free throw with 11:49 left. But the Jayhawks, led by Taylor, responded with an 11-0 run over the next six minutes to take control of the game.

Taylor’s first of two 3-pointers during the run — a straight-on make as the shot clock expired — sparked the Jayhawks, who scored on four of their next five possessions.

The Wildcats cut the deficit to 55-51 with 1:14 left on Rodney McGruder’s running jumper, and twice had a chance to inch closer in the final minute after Kansas missed a pair of free throws.

But both times, K-State came up empty — once when Withey blocked a shot at the rim, and again when Will Spradling misfired from point-blank range.

Jamar Samuels had a team-high 20 points and 12 rebounds for Kansas State, which trailed 28-18 at halftime after shooting just 22 percent in the first half. McGruder had 12 points and eight rebounds and Spradling added 10 points.

Angel Rodriguez, K-State’s freshman guard, finished with zero points and committed seven of the team’s 12 turnovers.

Thomas Robinson had 10 points and nine rebounds for Kansas, which won at Bramlage Coliseum for the 22nd time in its last 24 tries.

GAME NOTEBOOK: Nineteen of K-State’s 40 rebounds were on the offensive glass … Kansas improved to 19-15 in Big Monday road games since the Big 12’s inception in 1996 … Gipson was issued a technical foul with 4:09 left … Samuels tied a career high with four made 3-pointers.