Johnson opened the scoring with a 3-yard touchdown pass to Hunter Folkertsma. After Fred Coppet and Greene ran in short TDs, Johnson had a 4-yard sneak with 36 seconds left in the first half for a 27-0 lead.
Matt Domer capped the scoring with a 95-yard touchdown run - the second-longest TD run in school history - with 39 seconds remaining.
Coppet had 109 yards on the ground and Domer added 105 yards for Bowling Green (9-3, 7-1 Mid-American). Six Falcon rushers combined for 337 yards and five touchdowns.
Riley Neal was 24-of-40 passing for 154 yards with one touchdown and three interceptions for Ball State (3-9, 2-6).
Alfonso Mack, Eilar Hardy and Dernard Turner each had a pick of Neal.