Texas Teach came back from a 38-7 third-quarter deficit to pull off the biggest comeback in Division I-A bowl game history.
Woods scored the game winner on a three-yard run as Texas Tech bettered a 30-point comeback by Marshall against East Carolina at the 2001 GMAC Bowl.
Alex Trlica kicked a game-tying 52-yard field goal at the end of regulation for the Red Raiders (8-6).
Woods ran for three touchdowns and 108 yards on 19 carries, and Graham Harrell threw two touchdown passes on 36-of-55 completions for 445 yards for Texas Tech, which won two of its final three games.
Bryan Cupito passed for three touchdowns and 263 yards, and Amir Pinnix scored once and picked up 178 yards on 34 carries for the Golden Gophers (6-7), who had a three-game winning streak snapped.