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.
SMU has signed a second player from Australia, 6-foot-11 forward Harry Froling, to a national letter of intent. The Mustangs previously signed guard Tom Wilson from Australia.
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.