The Raiders (3-2, 2-0 Patriot) were trailing by 10 in the second quarter, but a 14-yard touchdown pass from Melville to Alex Greenawalt with four seconds left before the half cut the difference to 17-13.
Neither team scored until Melville's touchdown run with 11:21 to go gave Colgate its first lead of the day.
The Crusaders (2-4, 0-2) tried to respond on their next possession and drove 51 yards down the field in 10 plays. On third and 5 at the Colgate 22, Peter Pujals threw an interception - caught by Mike Armiento - to give Colgate the ball back with 7:35 to play.
The Raiders didn't give Holy Cross another chance and kept possession of the ball for the remainder of the game.