The Red Raiders (8-5) got their third straight bowl win to wrap up a month that began with coach Tommy Tuberville's abrupt departure for the job at Cincinnati. Texas Tech has hired Kliff Kingsbury to replace him, but interim coach Chris Thomsen led the team against Minnesota (6-7). Kingsbury was at the game, watching from a suite.
Doege threw for 271 yards and a touchdown and ran for another score in front of a crowd that included 1977 Heisman Trophy winner Earl Campbell and former Tech coach Spike Dykes.
Philip Nelson threw for 138 yards and two scores for the Gophers, who were in a bowl game for the first time since 2009.
The Red Raiders returned to a bowl after having their 18-season bowl streak snapped last year.
A 1-yard touchdown pass from Nelson to Drew Goodger gave Minnesota a 31-24 lead early in the fourth quarter.
Texas Tech led 24-17 at halftime, but couldn't do anything offensively in the second half until the last couple of minutes.
It was an ugly game for the Red Raiders, who had 13 penalties for 135 yards and lost the tight end Jace Amaro when he was ejected for throwing a punch.
Jakeem Grant ran for what was initially ruled a touchdown for Tech late in the third quarter. Amaro threw a punch at Derrick Wells in the end zone on the play and was ejected.
After the penalty, the play was reviewed and overturned. Doege threw an incomplete pass before Tech made a 32-yard field goal. But the Red Raiders had a false start penalty on the play and had to kick again and this time the Gophers blocked it.