Minnesota lost its sixth consecutive bowl appearance, but came close to a win thanks to touchdown passes on consecutive possessions in the fourth quarter by Mitch Leidner.
Those scores gave the Golden Gophers a 17-14 lead and they regained the ball after a missed Syracuse field goal attempt with a chance to run out the clock.
Syracuse, however, forced a Minnesota punt with two minutes to go and Brisly Estime returned the kick 70 yards to the Gophers' 14-yard line.
Facing third down and needing seven yards to pick up a first, Hunt went back to throw. He was flushed from the pocket and took advantage of a huge hole in the defense to sprint to the end zone for the winning touchdown.
Minnesota reached the Syracuse 40-yard line on its final possession, but two desperation passes by Leidner into the end zone fell incomplete.
Syracuse finished the season with a 7-6 record, winning its third straight bowl game and its fifth out of six.
Hunt completed 19-of-29 passes for 188 yards and ran for two scores. His 5-yard touchdown dash in the third period gave the Orange a 14-3 lead.
Leidner went 11-of-22 for 206 yards and two touchdowns. The Gophers finished 8-5 in a season that included consecutive wins over Northwestern, Nebraska, Indiana and Penn State.
The Gophers were the first of seven Big Ten Conference teams to appear in a bowl this season. The win for Syracuse gave the Atlantic Coast Conference a 2-1 bowl record with eight more teams from that league scheduled to see post-season action.