Colter completed 9-of-15 passes for 76 yards with a pair of interceptions and also carried the ball 12 times for 75 more on the ground as the Wildcats (10-3) logged their first bowl win since the 1949 Rose Bowl.
Venrick Mark, Trevor Siemian and Tyris Jones each ran for a touchdown as Northwestern finally emerged victorious after dropping nine consecutive post-season games.
Dan Vitale led the Wildcats' receiving corps with seven catches for 82 yards and Trevor Siemian completed 12-of-21 passes for 120 yards behind center in Northwestern's win.
The Bulldogs (8-5) struggled as Tyler Russell was limited to 12-of-28 through the air for 106 yards with four interceptions.
Mississippi State closed its season with five losses in six games.