The Red Raiders scored 10 points in the final 70 seconds and rallied for their third straight bowl win and their fifth in their last six post-season appearances.
That streak began with a comeback 44-41 victory over Minnesota in the 2006 Insight Bowl.
Minnesota took a 31-24 advantage early in the fourth period on a 1-yard throw from Philip Nelson to Drew Goodger and the Golden Gophers twice recorded interceptions in the final quarter to preserve the lead.
Texas Tech took over at its own 18 with 3:24 to play and quarterback Seth Doege needed seven plays to get the Red Raiders in the end zone. His touchdown throw of 35 yards to Eric Ward tied the game with 1:10 remaining.
Three plays after the kickoff, D.J. Johnson intercepted a Nelson pass and returned it 41 yards to the Minnesota 22. That set up Fyfe's field goal that allowed Texas Tech to end its season with an 8-5 record.
Texas Tech took a 24-17 halftime lead in a physical game that saw the Red Raiders called for five personal foul penalties and have one player ejected.
That ejection came during a bizarre series in the third period which saw one apparent Texas Tech touchdown negated by a penalty, another score wiped out by a replay decision, a go-ahead field goal disallowed because of a penalty and a second field goal attempt blocked
Doege completed 31-of-45 passes for 271 yards while Nelson went 7-of-16 for 138 yards with two touchdowns and the critical interception late in the game.
The Golden Gophers, who won their first four games of the season, lost four of their last five to wind up 6-7. They have lost their last five bowl games over the past eight seasons.
The Big 12 Conference has a 2-0 record in bowl games thus far. Minnesota was the first of six Big Ten teams that will take part in a bowl contest.