After Kansas State cut Texas' lead to 1, Isaiah Taylor hit a huge 3-pointer with 43 seconds left to put Texas up 69-65, then hit two free throws with 32 seconds left, putting the Longhorns up 71-67.
And after KSU freshman Barry Brown hit a 3-pointer with 20 seconds left to cut Texas' lead to 71-70, Javan Felix missed the front end of a 1-and-1 free throw opportunity with 14 seconds left.
But KSU freshman Dean Wade missed a 3-pointer for KSU with 2 seconds left, and Taylor grabbed the rebound to preserve the victory - despite severe foul trouble by Texas' bigs.
Prince Ibeh fouled out with 3 points, 0 rebounds, 0 blocks in 9 mins of action, and Shaq Cleare and Connor Lammert played much of the second half with four fouls.
That led to a lack of presence down low from Texas and allowed K-State to dominate the rebound battle (36-27, including 12 offensive rebounds to Texas' 5), the points in the paint (38-22) and second-chance points (10-2).
Whether it was Texas' defense or just an off night, the Horns benefited from a tough shooting night by KSU's Wade, who was 3-of-10 FG, 0-4 3PT and 3-of-7 FTs in 29 minutes.
But Taylor stepped up huge late in the game and led Texas with 19 points. Felix had 13 points (with 11 of those coming in the first half). Eric Davis added 10 points (with 8 of those coming in the first half) for the Horns, who improve to 18-10, 9-6 Big 12 and were listed as a No. 6 seed on Monday by ESPN bracketologist Joe Lunardi.
Important, huge win for Horns on the road after their lackluster loss to Baylor on Saturday. Now, Texas heads home with a little momentum heading into a big, seven-day stretch.
UP NEXT: ... Saturday at 1 pm CT at home against No. 3 Oklahoma (21-5, 9-5 B12).