The Gators (1-0) were clinging to a 17-14 lead when Driskel -- who gained 114 yards on 10-of-16 passing -- found Frankie Hammond on a 50-yard passing play to put the contest away.
Mike Gillislee scored two TDs and ran 24 times for 148 yards.
Bowling Green (0-1) got a 204-yard passing performance from Matt Schilz, who completed 24-of-49 with an interception.
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