And that's precisely what Texas did, ending both strings in a 74-63 victory that saw the Longhorns weather an early storm and run away with the game late.
"It was a great win for our program," said Texas coach Rick Barnes afterward. "I can't tell you how much respect I have for Bill (Self). He's one of the best. He's the model of consistency and one of the best. To come up here and get a win -- we've had so many great games with him where we've obviously come out on the other end."
The game was a bruise fest and was high on emotion, one with 44 fouls, including four technicals, and protracted long defensive streaks. Kansas jumped out to an early advantage, leading by as many as 15 points and taking a 35-23 advantage into the locker room by holding Texas to 30.8 percent from the field.
But in the second half, the Longhorns put together a long defensive string of their own, holding Kansas to a 3-19 stretch from the field at one point while heating up offensively thanks to J'Covan Brown. Brown, who scored 28 in a contest against Kansas last year, helped the Longhorn offense heat up, keying a 13-2 run with a pair of three-pointers.
That burst put Texas up for the first time in the game, 45-44 with 10:39 left in the contest. The lead bloomed into double digits when Cory Joseph banked in a three-pointer as the shot clock expired, putting the Longhorns up 59-48 with 5:17 remaining. The lead reached its zenith at 12 points twice, at the latest when a Jordan Hamilton jumper found its mark with 3:46 left, giving Texas a 63-51 advantage.
Kansas fought back over the next minute, closing to within six at 64-58 with 2:29 remaining. But Kansas never game any closer than 66-61. After Gary Johnson made a jumper, Hamilton stopped the Jayhawks by swatting a Tyshawn Taylor shot that was scooped up by Joseph. The Longhorns shot 6-6 from the free throw line down the stretch to seal the win.
The Longhorns won the second half 51-28 by shooting 63.6 percent from the field, 66.7 percent from behind the arc and making 19-of-23 (82.6 percent) second-half free throws. Kansas meanwhile, shot 26.7 percent and 18.2 percent, while making just 10-of-17 (58.8 percent) of their free throws.
The Longhorns were led by 23 points from Brown, while Hamilton chipped in 17 points and nine rebounds. Tristan Thompson had 12 points and five blocks, and Joseph had 11 points and nine boards.
Tyrel Reed led the Jayhawks with 17 points and grabbed six rebounds. Marcus Morris scored 16 points and grabbed seven rebounds, while Markieff Morris had 10 points and five boards. But the twins had a cold shooting day, making just 8-of-24 shots from the field, 1-6 from three and 9-16 from the free throw line.
The Longhorns moved to 16-3 and into sole possession of first place in the Big 12 with a 4-0 conference record. Kansas fell to 18-1 and 3-1 with the loss.