Webb entered the game at the end of the third quarter when starter Baker Mayfield went down with an apparent knee injury, and completed 3-of-6 passes for 36 yards.
Ryan Bustell ran for a 31-yard TD in the fourth quarter for Tech (5-0, 2-0 Big 12), who had trailed 10-0 at the end of the first quarter. Eric Ward caught seven passes for 122 yards and a score.
Texas Tech gained 114 yards on the ground and 404 in the air. Kansas (2-2, 0-1) tallied 273 total yards of offense.
Jake Heaps completed 16-of-32 passes for 189 yards for the Jayhawks. He completed a 25-yard TD pass to Jimmay Mundinein the first quarter. Kansas did not score again until Andrew Turzilli caught a 28-yard TD pass from Michael Cummings with 7:43 left in the game.
Mayfield threw for 368 yards before hurting his right knee. His status was not immediately known.