The defensive-minded Jayhawks, with Travis Releford on the perimeter and Jeff Withey in the paint, make life miserable for opposing offenses, while the veteran Wildcats relish the chance to bump, bang and bludgeon foes on both ends of the court.
Little surprise that they played another tough-as-nails game Tuesday night.
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Releford scored 12 points, Withey and Ben McLemore each added 11, and the third-ranked Jayhawks held on down the stretch for a 59-55 victory that gave them sole possession of first place in the Big 12.
"That game went just as all you predicted, not the most artistic," Kansas coach Bill Self said, sporting the kind of wry smile that said he didn't mind one bit.
The Jayhawks have grown accustomed to such blood-and-guts games, needing a desperation 3-pointer from McLemore to force overtime in a win over Iowa State and a frantic second-half comeback to beat Texas, all while running their winning streak to a nation-leading 16 games.
Kansas (17-1, 5-0 Big 12) briefly led by 10 points in the second half before needing everything it could muster in the closing seconds to end the Wildcats' eight-game winning streak.
"They just find ways to win," Kansas State coach Bruce Weber said.
Shane Southwell, who had a career-high 19 points, tried to do the same for Kansas State (15-3, 4-1), getting his team within 56-53 with a scooping layup with 38.2 seconds left.
Naadir Tharpe made two foul shots to restore the Jayhawks' five-point lead, and the Wildcats' Rodney McGruder misfired from beyond the arc at the other end. But McLemore missed the front end of a 1-and-1, and McGruder's two foul shots made it 58-55 with 5 seconds left.
Elijah Johnson was fouled, and his free throw put the game away.
"There were several plays that allowed us to keep our distance," Self said. "We made it hard on ourselves by not converting at the free throw line and stuff like that, but just a tough game and a great road win."
McGruder finished with 13 points and Angel Rodriguez had 12 for the Wildcats, who lost for the 45th time in the last 48 games against their bitter in-state rival.
Kansas improved to 23-2 in Bramlage Coliseum since its opening in 1987.
"If anything, we look forward to this game," Withey said. "It's a lot of fun, a hostile environment. It's one of the best crowds we're going to get besides our own crowd."
The atmosphere was amped long before the opening tip. Students on their first day back from winter break lined up for several hundred yards in freezing temperatures, and then flooded seats on one side of the building more than 2 hours before the game started.
The Jayhawks, undaunted by the pulsating crowd, methodically built a 16-8 lead midway through the first half. Kansas took advantage of some balky outside shooting by the Wildcats, and routinely beat them off the dribble at the other end for easy baskets around the rim.
McLemore picked up his second foul of the half with 9:22 left, though, and Kansas State went on a run with the Jayhawks' leading scorer on the bench. Martavious Irving started the 11-2 spurt with a scooping layup and Southwell ended it with a 3-pointer for a 19-18 lead.
Self called a timeout and it settled down the senior-laden Jayhawks.
Perry Ellis scored a couple of baskets around a shot clock-beating jumper by Tharpe to help Kansas retake the lead, and Kevin Young's putback off his own miss made it 31-27 at halftime.
McGruder, shadowed everywhere by Releford, only managed two points on a soaring jam just before halftime. He missed both of his outside shots as the Wildcats went 4 for 16 from the arc.
The Big 12's reigning player of the week finally hit a 3 to start the second half, but Kansas answered with eight straight points, including a dunk by Withey off a feed from Young that forced Weber to call a timeout of his own early in the half.
McGruder hit back-to-back 3s later in the half to help keep the Wildcats close, but a 3 from the corner by McLemore and then an open jumper by the freshman with 6:50 to go gave the Jayhawks a 53-43 lead, the first time the margin had reached double figures all game.
Southwell shot the Wildcats back in it, hitting a jumper with 8:13 remaining and then consecutive 3-pointers -- his fourth and fifth of the game -- to make it 54-49 with 5:30 remaining.
But the Jayhawks kept buckling down on defense, kept finding an answer for every push that the Wildcats made, allowing them to pull out a victory despite a scoring a season-low 59 points.
"I'm upset we lost that game. This is the last time I'm going to play them in Bramlage," McGruder said. "But we have a lot of basketball left. This can't be the end of it right here."