Cooper scored a pair touchdowns on 25 carries for the Pirates (10-3), who completed just their second season ever with a double-digit win total.
Shane Carden made good on 29-of-45 throws pass attempts en route to 273 yards and with a score and also received a TD pass as East Carolina notched its first bowl victory win since 2007.
The Conference USA champs also got a rushing score from Breon Allen and a Cam Worthy touchdown grab.
Tyler Tettleton was picked off three times for the Bobcats (7-6), completing 21-of-40 passes for 228 yards with a touchdown to Donte Foster.
Foster posted 160 receiving yards on six catches for Ohio.