Cook threw for 143 yards overall and Langford rushed for 134 yards for the Spartans (11-1, 8-0 Big Ten).
Michigan State won its final eight games of the season and will face Ohio State in next week's Big Ten championship game.
Minnesota (8-4, 4-4) held the ball for 38 minutes, 41 seconds compared to 21:19 for the Gophers, but Minnesota only managed a 34-yard field goal by Chris Hawthorne late in the second quarter to cut Michigan State's lead to 7-3.
David Cobb ran for 101 yards for Minnesota, which had not won eight games since 2003. Phillip Nelson passed for 77 yards and was intercepted twice.
Celebrity Couples of 2014 [PHOTOS]