The Bears (8-12, 4-5) won the rebound battle 37-25 and outscored the Bison 30-10 in the paint.
Chiles added seven rebounds and three blocks while Justin Black grabbed eight boards to go with 13 points.
Howard (6-18, 3-7) trailed 26-25 early in the second half, but took a 39-32 lead with 13:14 left on Anton Dickerson’s 3-pointer.
Chiles responded with a layup seconds later, and Morgan State ran off 11 consecutive points, including Black’s go-ahead tip-in with 6:54 remaining.
Mike Phillips led Howard with 19 points, and Dickerson had 17.
The victory was Morgan State coach Todd Bozeman’s 100th in the MEAC, the most by any Bears’ coach.
The meeting was the 100th all-time between the schools, with Morgan State holding a 59-41 advantage.