Taylor Barnette scored 20 with 5 of 14 3s and the Bruins (9-6, 1-0) made 17 of 39 from long distance (44 percent).
Evan Bradds scored 13 points and grabbed 14 rebounds for Belmont, which trailed early but led 47-44 at halftime.
The Redhawks tied it at 49 on Tony Anderson's layup early in the second half, but Belmont pulled ahead on a 15-4 run in which Nick Smith made back-to-back 3s for a 64-53 lead with 12:31 left. Isiah Jones' 3 pulled the Redhawks within 86-80 with 37 seconds left, but Barnette, Bradshaw and Adam Luke combined for six free throws in the remaining 30 seconds to seal it.
Jones scored 20, Eric McGill added 15, and Antonius Cleveland had 13 with 11 rebounds for the Redhawks (2-11, 0-1).