Brown was 6 of 12 from the floor, though he missed all five of his 3-point attempts. He also went 7 of 11 from the line.
UAB (4-6) built a 41-35 lead at the half behind nine points from Nick Norton, all coming on 3-pointers.
UNC Asheville (4-5) mounted a comeback in the second half and took a one-point lead with 10:07 left on Andrew Rowsey's layup. But Brown scored eight in a 13-3 run for the Blazers and Asheville never countered.
Asheville's David Robertson had 15 of his team-high 22 points in the first half. He was 4 of 9 overall on 3-pointers. Rowsey added 18 points with six assists.
UAB was 27 of 35 from the line, while Asheville made 13 of 16.