Toledo (24-5, 12-4 Mid-American) trailed by 13 after half before battling back and finishing regulation on a 14-2 run.
Drummond tied the game at 75 on a put-back layup. A five-second inbounds violation gave possession to Toledo before Jonathan Williams hit two free throws to give Toledo its first lead, 77-75.
Toledo opened OT on a 5-0 spurt and outscored Western Michigan 19-8 overall.
Brown had 18 points and 10 assists. J.D. Weatherspoon (14), Nathan Boothe (13) and Rian Pearson (11) also scored in double figures.
David Brown scored 29 for the Broncos (19-9, 12-4). Shayne Whittington had 25 points and 13 rebounds.