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.
SEC Network visits Knoxville to delve into Tennessee's '25 points' mantra, which represents the combined difference in the Vols' previous five losses.
SEC Network's Dari Nowkhah and Greg McElroy talk life and football with Tennessee's Butch Jones at the head coach's favorite Knoxville staple.
How the hardships of picking oranges and tomatoes in the fields of Florida delivered Clemson star Mackensie Alexander to the NFL's doorstep.
SEC Network's Maria Taylor, Marcus Spears and Kevin Weidl discuss the former Mississippi State QB's potential with the Cowboys.
SEC Network's Maria Taylor, Marcus Spears and Kevin Weidl discuss the fit for QB Brandon Allen at Jacksonville and RB Jonathan Williams at Buffalo.
SEC Network's Marcus Spears and Kevin Weidl discuss the SEC players that will have the biggest overall impact in the NFL.