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.
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.