The Bruins (16-7, 7-1 Ohio Valley) shot 52 percent from the field. Reece Chamberlain had 14 points and seven assists.
Eastern Kentucky (14-7, 5-3) was led by Glenn Cosey with 22 points. Corey Walden chipped in 21 and Eric Stutz had 14 with 11 boards for the Colonels.
Mann hit a late 3-pointer in the first half to give Belmont a 50-30 halftime advantage. A Chamberlain layup put the Bruins up 64-42 at the midway mark in the second half.
The Colonels stormed back within five after two free throws and a layup by Walden, but Chamberlain responded with a pair from the line and Bradshaw made a layup with 32 seconds left.
After a late free throw by Mann, Cosey hit a 3-pointer for the final margin.