Ian Clark led Belmont (5-3) with 24 points, and Keron Johnson scored 11. The Bruins hurt their cause with 24 turnovers, and they shot only 4 of 6 from the foul line.
The Rams shot 15 for 22 from the line and outrebounded the Bruins 34-23.
Belmont made up ground in the second half after trailing 39-21 at the break. From a 43-27 deficit, the Bruins knocked down three 3-pointers to help close the gap to 50-44 at the 13:27 mark.
Belmont's Reece Chamberlain's 3-pointer to close to 66-61 at 4:46, but VCU's Brandenberg made a 3-pointer for a 71-63 advantage at 3:16, and the Rams held on.