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.
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.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.