The Buckeyes shot just 35 percent from the field and made a mere 3-of-15 from 3-point range, but they recorded 15 steals and forced 26 turnovers in all.
Ohio State led by only five at half and needed to finish the opening period on an 11-3 run to do that. The Buckeyes then started the second half with a 9-4 surge.
Shannon Scott added 13 points and nine rebounds in helping Ohio State improve to 4-0.
American (1-2) was led by Tony Wroblicky with 14 points and seven rebounds.