The first of those two scores was a 60-yarder that capped a 17-point third quarter for the Falcons (3-3, 1-1), who trailed 10-0 at halftime.
Bowling Green held the Zips (1-5, 0-2), who gained 280 first-half yards, to 36 in the second half.
Anthony Samuel, who carried 15 times for 117 yards, started the Falcons off quickly in the third quarter with runs of 27 and 20 yards on the first two plays from scrimmage. Bowling Green had 144 rushing yards in the third quarter as it won for the 500th time in the program's 94 seasons against 349 losses and 51 ties.
Akron's Dalton Williams, who was averaging 335.8 yards passing, was held to 228, completing 29 of 50, including a touchdown.
Miami has lost running back Gus Edwards for the entire season because of a left foot injury.
Virginia Tech will wear a decal on its helmets against No. 1 Ohio State on Monday night to honor slain Roanoke television journalists Alison Parker and Adam Ward.
South Carolina football players will wear stickers on their helmets this season to honor the nine people who died in a shooting at Emanuel AME Church in Charleston this past June.
Washington has found its starting quarterback, but coach Chris Petersen said the Huskies will keep that information under wraps until Friday's season opener at No. 23 Boise State.
Joey Counts scored on a 1-yard run on fourth-and-goal with 2 seconds left to give Montana a 38-35 victory over four-time defending FCS champion North Dakota State on Saturday.
Transfer Vernon Adams will be the starting quarterback when Oregon begins its season against Eastern Washington on Sept. 5.