Richie made four of Western Michigan's seven 3-pointers and Haymond hit eight of the Broncos 20 free throws.
David Brown and Drake LaMont scored 10 points apiece as Western Michigan (13-5, 4-1 Mid-American) won back-to-back games on the road. Connar Tava, the only Broncos starter not in double-figure scoring, had nine points and 10 rebounds.
Western Michigan trailed 23-21 at the break.
Haymond's three-point play capped a 10-2 run for a 45-37 lead with 10:49 left. Later, Richie hit a 3-pointer to start an 8-2 spurt for an 11-point lead with 45 seconds left and Haymond made 5 of 6 free throws in the final 37 seconds.