Patterson's boot came after a 17-yard catch from Nick Harwell and Spencer Treadwell's 30-yard run on the decisive scoring drive.
Zac Dysert's 21-of-36 passing for 311 yards with a touchdown and interception helped the RedHawks (4-4, 3-1 MAC) snap a two-game losing streak.
The Bobcats (7-1, 3-1) were bounced for the first time this season despite getting a 302-yard passing performance from Tyler Tettleton, who also had a rushing touchdown.
Ohio had been off to its best start since going 10-0 in 1968.
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