Jamell Harris grabbed 10 rebounds for the Eagles (8-10, 3-1 Mid-American), who won their second in a row.
Western Michigan enjoyed a nine-point lead at 35-26 early in the second half.
But Sims' 3-pointer tied it 50-50 with 59 seconds to play. Green's 3-pointer gave Eastern Michigan a 53-50 edge with 5 seconds left - its only lead in regulation - before Hutcheson drilled a 3-pointer at the buzzer to force overtime.
Stainbrook put the Broncos ahead early in overtime, but then DaShonte Riley, Green and Harris hit consecutive baskets to give the Eagles a 59-55 lead with 1:21 left.
Eastern Michigan helped offset 37.7 percent shooting (20 of 53) by making 8 of 17 3-pointers.
- Sports & Recreation
- Sports & Recreation/Basketball
- Eastern Michigan