The Bobcats (3-0) took control with an 18-3 run that put them ahead 26-11 with 5:49 left in the first half.
Ohio shot 60.9 percent (14 of 23) in the half while holding the Terriers (1-3) to 14.3 percent (3 of 21).
It was 34-16 at halftime. Ivo Baltic's jumper made it 36-16 to start the second and the Bobcats never led by fewer than 20 points the rest of the way.
Ohio, which has won 12 straight at home, has won its three games this season by an average of 30 points.
Cooper, a senior guard, had two steals for Ohio to become the school's all-time leader with 261.
DouDou Gueye, a 6-foot-10 center from Senegal, has signed with Ball State as a graduate transfer from South Carolina State.
Duke freshman point guard Derryck Thornton Jr. is transferring to USC, his father announced on Friday to Scout.com.
We have changes at the top of the draft and a shakeup in the lottery, with teams starting to make their final decisions. Get the latest in Chad Ford's Mock Draft 9.0.