Bradds was 8 of 8 from the floor and 6 of 7 from the line. Bradshaw finished on 9-of-16 shooting and had six assists and three steals.
Taylor Barnette scored 14 points, Tyler Hadden had 13 and Reece Chamberlain seven points with eight assists for Belmont (11-7, 3-2 Ohio Valley), which shot 34 of 57 for 59.6 percent from the field, and made 10 of 22 from deep.
Austin Peay overcame a 15-point second half deficit to pull within 82-77 with 2:17 to play. Barnette hit a jumper and the Bruins made 5 of 6 from the line to seal it.
Chris Horton had 23 points and 12 rebounds to lead Austin Peay (6-12, 1-3).