The Bobcats helped offset 19 turnovers with a 45-33 edge on the boards, led by Antonio Campbell with 15.
The game was tied at halftime. After falling behind by four to open the second half, the Bobcats scored the next eight points and wouldn't trail again.
A 10-0 run, including four points apiece from Simmons and Wadly MomPremier, gave Ohio a 62-48 lead. Marshall cut it to nine once after that, but Ohio used a 10-1 run for a 19-point cushion with a minute to go.