Cooper made 7 of 9 shots from the field, including a season-high five 3-pointers, and dished out seven assists for Ohio, which is averaging 25 assists over its last five games.
Keely, who hit 6 of 10 shot attempts, converted a season-high seven free throws. His shot from the stripe with 1:52 left in the first half gave Ohio (10-5, 1-0) a 48-31 advantage and Cooper hit a 3-pointer and two free throws to give the Bobcats a 53-31 lead at the break.
Ohio extended its lead to 64-36 on another trey from Cooper.
The Bobcats shot 50.8 percent (32 of 63) from the field and hit 9 of 18 3-point attempts.
Javon McCrea and Jarryn Skeete scored 13 apiece for Buffalo (5-10, 0-1).