Scott was 11-for-21 for 132 yards and a 7-yard touchdown pass to Terrence McRae with 10:56 left for the Bobcats (4-2, 2-0 Mid-American Conference).
Zips quarterback Matt Rodgers injured his knee late in the second quarter when he fumbled at the 3 and Ohio's Patrick Tafua recovered in the end zone.
Rodgers, who was 10-for-19 for 89 yards and had 11 rushes for 80 yards, will be evaluated Sunday or Monday. He was replaced by Patrick Nicely, who saw his first action for Akron (1-4, 0-2).
Ohio's Matt Weller kicked the first of his two 27-yard field goals for the only first-half scoring. Payne's blocked punt came with 10:49 left in the third quarter for a 10-0 lead, then Joe Tuzze's 3-yard run made it 10-7.