Keely was 8-of-12 shooting, while Cooper had 16 points, 10 assists and five steals. Nick Kellogg added nine points and Ivo Baltic had eight points and nine rebounds for the Bobcats (20-6, 11-2), who have won 12 of their past 13.
The win was Ohio's 19th consecutive in home MAC games. The Bobcats had 23 assists, upping their team average, which was tops in the country at 18.7.
Ohio hit its first seven shots and led 17-3.
The Eagles (12-14, 5-7) were coming off their first road win of the season, 56-50 over Ball State. J.R. Sims paced Eastern Michigan with 12 points as the team shot 27.6 percent (16 of 58), including 29.4 percent (5 of 17) from 3-point range.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.