Bramble ran in for the first touchdown of the game and his 2-yard score in the second half kept the Big Green within striking distance. Bo Patterson's 20-yard touchdown reception put Dartmouth ahead for good, and McManus stretched the lead to 28-19 on a scoring dive with 5:39 left in the third.
Dartmouth was the last Division I football team, including FBS and FCS, to hold its season opener.
Nick SanGiacomo completed a touchdown pass to Joey Fields for the Blue Devils (1-3), marking their first score of the second half with 7:13 left to play. The touchdown put an end to the Big Green's four-touchdown scoring spree.
The game was the first matchup between the two schools.