Eric Norman made a layup with 4 minutes left, pulling Montana State within three, 54-51, but Shanks made two free throws and, after a Montana State turnover, Dustin Hobaugh hit a 3-pointer to push the North Dakota lead to eight with 2:16 remaining.
A four-point play by Danny Robison pulled Montana State (3-10) to 61-56 with 1:39 to go. After getting a stop on the other end, the Bobcats called timeout before turning it over on a five-second violation.
A layup by Shanks with 43 seconds left gave North Dakota a 63-56 lead and Estan Tyler and Hooker each hit two free throws down the stretch to seal it.
Michael Dison led Montana State with 22 points.