The Ohio offense went three-and-out on its first two possessions while Central Michigan (3-3, 1-1 Mid-American) used drives of 77 and 68 yards, both of which were capped by touchdown passes from Cooper Rush to Davis, to take a 14-0 lead.
With 33 seconds left in the half, Ohio's Kylan Nelson recovered a fumble - forced by Tarell Basham's strip sack of Rush - and gave Ohio (3-3, 1-1) first-and-goal at the five. The Bobcats settled for a Josiah Yazdani 24-yard field goal.
Rawls scored on a 15-yard run, capping 15-play, 75-yard drive to open the second half and Ohio never threatened again.
Davis moved into 4th on Central Michigan's career receiving yards list with 3,040.