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.