Texas erased a 23-3 second-half deficit with three unanswered fourth-quarter touchdowns, taking its first lead at 24-23 with 51 seconds left.
Arch Manning steadied the comeback after early turnovers and missed chances, while Hollywood Smothers scored all three late touchdowns, including the go-ahead plunge after a goal-line review.
Ohio State controlled most of the game behind Julian Sayin and Jeremiah Smith and led 20-3 at halftime, but a missed 45-yard field goal kept Texas within one score.
Graceson Littleton sealed the upset with an interception in the final seconds, giving Steve Sarkisian a breakthrough win over a program that had repeatedly blocked Texas' title path.