The Bobcats (13-3, 1-1) never trailed, jumping out to a 12-0 lead and taking a 31-25 advantage into halftime.
The Bulls (8-5, 1-1) got to 33-30 with 15:07 remaining, then Ohio pulled away with an 11-0 spurt, capped by a Cooper three-point play.
Neither team shot well, with Buffalo (8-5, 1-1) outshooting the Bobcats from the field 38 percent (19 of 50) to 32.2 percent (19 of 59).
Ohio, which came in ranked sixth in the nation in turnover margin, scored 22 points off 23 Bulls turnovers while committing 15 miscues.
Mitchell Watt's 18 points led Buffalo, whose 52 points were a season low. Bulls leading scorer Javon McCrae (17.3 points per game), scored only eight points on 4-for-13 shooting.
The Bobcats lead the series 23-8.