Warren was stopped at the 3-yard line on his winning score, but kept his feet moving, pulling the pile of Texas and Kansas State players along for the ride before crossing the goal line.
After two holding penalties on their possession in the second overtime, the Wildcats' Matthew McCrane's 53-yard field goal attempt hit midway up the left upright and fell back into the end zone, allowing Texas (3-2, 2-0 Big 12) to win on its possession.
Longhorns quarterback Sam Ehlinger hit former QB Jerrod Heard on a 25-yard TD pass on the first play of overtime to give Texas a 34-27 lead.
Backup quarterback Alex Delton, who entered the game late in the third quarter when Kansas State starter Jason Ertz was dinged up, then ran 8 yards to the tying touchdown in the first overtime period, sending the game to a second extra period.
Delton led the Wildcats (3-2, 1-1) to a game-tying drive that was capped by his 2-yard TD run with 3:37 to play in the third quarter. He then ran for 11, 13 and 22 yards and hit Dalton Schoen on a 23-yard pass on Kansas State's ensuing possession, which ended in McCrane's 33-yard field goal that staked the Wildcats to a 27-24 lead early in the fourth quarter.
Texas' Joshua Rowland hit a 34-yard field goal with 1:37 remaining in regulation to tie the contest at 27 but missed a 45-yard attempt with 2 seconds remaining that would have won the game for the Longhorns in regulation.
Rowland's tying kick came after he missed a 27-yard attempt on Texas' previous possession.
Ehlinger, a true freshman, was named the starter an hour before game time and responded by passing for 380 yards and rushing for a team-high 107 yards on 20 carries.
McCrane line-drived a career-high 54-yard field goal to open the scoring before Ertz (224 yards passing) and Schoen, a sophomore walk-on, connected on touchdown passes of 82 and 12 yards in the first half for the Wildcats.
Texas countered with two 1-yard TD runs from Kyle Porter and an Ehlinger-to-Warren 33-yard scoring pass that allowed the Longhorns a 21-17 lead at halftime.
Rowland converted a 34-yard field goal on Texas' first possession of the third quarter to expand the Longhorns' advantage to 24-17.