The Bruins (16-7, 7-1 Ohio Valley) shot 52 percent from the field. Reece Chamberlain had 14 points and seven assists.
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.
Former Michigan point guard Spike Albrecht will play for Purdue as a graduate transfer next season.
Only six major-conference teams have failed to win an NCAA tournament game since the turn of the century. When will each program snap the streak?
Bruce Weber's Kansas State team earned a share of the Big 12 title three years ago, but a lot has changed since then and the pressure is on.
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