Peter Suder scored 18 points for the RedHawks before fouling out with just over seven minutes remaining. Almar Atlason added 16 points, Perry finished with 14 and Eian Elmer 10.
Jayden Brewer led Western Michigan (10-19, 4-12) with 19 points and 11 rebounds. Justice Williams and EJ Ryans each added 14 points.
Miami is used to playing close games and won for the seventh time this season by less than six points.
The RedHawks trailed by four points, 30-26, at the half and fell behind by eight points twice early in the second half before tying the game at 49-all with 11:02 remaining.
Western Michigan ran off eight straight points for a 57-49 advantage with 8:40 remaining and led by nine (59-50) with 6:38 left before Miami chipped away and moved ahead 66-65 on a layup by Antwone Woolfolk with 14 seconds left.
Elmer's free throw with 37 seconds remaining gave the RedHawks a 67-65 edge, but Western Michigan tied it with 11 seconds left on a basket by Williams before Perry made the game winner.
Up next
Miami (Ohio): Host Toledo on Tuesday.
Western Michigan: Host Ball State on Tuesday.
___
Get poll alerts and updates on the AP Top 25 throughout the season. Sign up here and here (AP News mobile app). AP college basketball: https://apnews.com/hub/ap-top-25-college-basketball-poll and https://apnews.com/hub/college-basketball