Playing at home for the first time in a month, Western Michigan built an 11-point lead through the first half, but the Bulldogs rallied early in the second, cutting the margin to just four, 39-35, after a Ladarius Tabb dunk with 12:45 left. After a layup by Tabb with 3:59 left made it 57-52, Brown knocked down a 3 and put up seven straight points.
Tucker Haymond scored the last six points for the Broncos, dunking with 56 seconds left and adding four straight free throws.
The Broncos (7-4) shot 54.8 percent from the field (23 of 42) and were 20 of 26 from the free throw line.
Tabb had 17 points to lead Alabama A&M (1-8), which shot 51.1 percent (24 of 47).