D.J. Cooper, who finished with 13 points, sank three free throws in the final 9 seconds to clinch the win for the Bobcats (15-4, 3-2 Mid-American Conference).
Miami led 37-31 at halftime and 63-57 with 3:08 left in the game before Ohio started its run. Cooper knocked down a 3-pointer with 3 minutes to play, sparking a 9-0 Bobcats run that would give them the lead for good.
Nick Kellogg scored his only two points on free throws with 18 seconds left, starting a stretch of five Bobcats foul shots in the final seconds to hold onto their win. Ohio has won three of its last four contests.
Brian Sullivan scored 16 points to lead the RedHawks (5-12, 1-4), who have lost five of six.