Cooper had 11 points and 10 assists for the Bobcats (7-6), who had their second-highest point total of the season behind a 112-107 four-overtime loss to St. Bonaventure on Dec. 18.
They also allowed a season low for points and field goals (18) and tied a season high with 48 rebounds.
After Norfolk State (1-10) scored the opening basket, Ohio used an 8-0 run to pull ahead for good. The Bobcats led by 21 in the first half before taking a 38-23 lead into the break.
Ohio shot 51.7 percent from the field (30 of 58) while the Spartans shot only 32.1 percent (18 of 56).
Pendarvis Williams led Norfolk State with 13.