Minnesota's Rodrick Williams Jr. scored on a 2-yard run to give the Gophers a 10-7 lead in the first quarter.
Doege lost his helmet on a 5-yard scramble on Tech's next drive and had to go out for one play. He was replaced by Michael Brewer, who found Derreck Edwards for a 13-yard touchdown pass to give the Red Raiders a 14-10 lead.
Minnesota's Troy Stoudermire returned the opening kickoff 26 yards to break the NCAA record for career kickoff return yards. He finished the game with 111 yards to push his total to 3,615.
The Gophers ended that drive with a 41-yard field goal to make it 3-0.
Texas Tech's Grant returned the ensuing kickoff 99 yards for a touchdown to put Texas Tech up 7-3.