It was Ohio's third double-digit win over the season and raised the Bobcats' record to 4-2. Marshall dropped to 0-4 with the loss.
The 'Cats shot 50.8 percent from the floor, including 56.3 percent in the second half. Ohio held a 12-6 advantage in second-chance points and 12-4 edge on fast break points.
Junior forward Wadly Mompremier contributed eight points and seven rebounds and added three blocks in 15 minutes of work off of the bench.
Redshirt freshman guard C.J. Burks led Marshall with 20 points on 9-of-17 shooting. He also posted a steal.
Senior forward James Kelly added 18 points, eight rebounds and two steals in 23 minutes for the Herd.
Marshall raced out to a 9-1 lead at the 16:21 mark, taking advantage of three early Bobcat turnovers. The Herd held on to the lead until the 1:15 mark of the first half, when Ohio tied the game at 34-all on a layup by Simmons.
With a pair of free throws by Simmons with one second remaining in the first half, Ohio and Marshall entered halftime knotted up at 36-all.
Simmons and Kaminski led the Bobcats with nine points in the opening frame, while Campbell hauled in a half-high 10 rebounds -- including five on the offensive end. Marshall guard C.J. Burks led all scorers in the first half with 12 points.
After falling behind 40-36 in the opening minute of the second half, Ohio used a 26-8 run to grab its first lead of the game at the 18:07 mark and a 62-48 advantage with 10:03 remaining in the game.
The Bobcats maintained a lead for the rest of the contest, extending their advantage to as much as 19 with 1:01 to go in the contest. Simmons tallied 10 points in the final 10:03 of the game.