Green scored for the first points of the game and added a 50-yard touchdown run in the third quarter for the Spiders (2-1), who saw their lead dip below 10 points once over the final three quarters.
Richmond's defense held Hampton to just 281 yards of total offense, while not allowing a single Hampton player to reach the 100-yard plateau.
Jaylian Williamson threw for 88 yards for the Pirates (0-3), before being relieved the second half in favor of Bryan Bailey. Hampton's first touchdown came 30 seconds into the second quarter, when Williamson found Rashawn Proctor on 13-yard strike. The Pirates would not score again until the final minutes, getting a 12-yard touchdown run from Eric Carter Jr.