Jackson was 9-for-14 for 76 yards and had TD passes of 5, 7 and 6 yards, the last two to Jordan Thompson. Jackson also rushed for 53 yards for the Bobcats (3-3, 2-1 Mid-American Conference).
Jackson's second touchdown pass was the 27th of his career, moving him into second place all-time for Ohio behind Cleve Bryant (1967-69) with 29.
Ohio led 28-3 at halftime, then Bates had TD runs of 62 and 12 yards and Donovan Fletcher scored on a 55-yard interception return.
Bowling Green (1-5, 0-2) recovered a fumble on Ohio's first drive but could not score on fourth-and-goal at the 1.