Trey Norris scored 10 points and the Coyotes (5-8) converted 17 Montana fouls into 13 of 18 free throws.
South Dakota led for much of the first half, but the Grizzlies hit consecutive 3s in the final 1:20 and to take a 37-33 halftime lead.
Chris Kemp hit back-to-back layups amid a 12-6 run and the Grizzlies extended their lead to 49-39. The Coyotes rallied and led 58-57 after Norris hit a pair of free throws. Larson tied it at 62 with a layup, then put South Dakota ahead for good with the first of two free throws as part of an 8-0 run the Coyotes used to finish the game.
Jordan Gregory led Montana (3-7) with 18 and Kemp had 12.