Marcus Colbert's 3-pointer had lifted Montana State into a tie with 36 seconds left.
Bos finished with 17 points while Tyler Larson added 12 points, including 8-of-10 shooting from the free-throw line, and 11 rebounds for his fifth double-double this season. Trey Norris scored 10 points for the Coyotes (4-8), who snapped a four-game losing streak.
Colbert led Montana State with 21 points. The Bobcats (3-6), playing in Vermillion for the first time since 1946, remained winless in six road games.
Bos hit three consecutive 3-pointers to give the Coyotes a 36-28 lead with 16 minutes left. The lead held until the 5:32 mark when Colbert made a 3-pointer for a 44-43 MSU lead. Neither team led by more than four after that.