The Thundering Herd (2-1) trailed 7-0 at halftime after Bowling Green's Chris Wright caught a 50-yard touchdown pass from Tyler Sheehan, who completed 43-of-62 passes for 383 yards.
But Marshall answered with 17 straight points and never fell behind again. Brian Anderson connected with Antavio Wilson on an 11-yard touchdown, Marshall scored on his long run and Craig Ratanamorn made a 31-yard field goal.
Anderson completed 11-of-21 passes for 100 yards and threw one interception.
Bowling Green's Freddie Barnes broke a school record with 17 receptions, finishing with 109 yards receiving for the Falcons (1-2). Wright caught five passes for 104 yards.