Joel Monroe kicked a 32-yard field goal to put Minnesota up 41-38 in overtime, but Shannon Woods scored on a three-yard run to win it for the Red Raiders.
The previous record for a bowl comeback was 30 points, set by Marshall against East Carolina in the 2001 GMAC Bowl.
Texas Tech (8-6) appeared finished after Minnesota (6-7) took a 38-7 lead with 7:47 to go in the third quarter. But the Red Raiders mounted a furious comeback, scoring 31 unanswered points in less than 20 minutes.
Alex Trlica's 52-yard field goal as regulation expired sent the game into overtime.
Quarterback Graham Harrell had 445 yards passing.