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.
There's nothing to suggest the Jayhawks won't end up atop the Big 12 for a 13th season in a row. But what about a return to the Final Four?
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.