Curley, who was 23 of 31 for 305 yards, connected with Mark Layton on a 17-yard touchdown for the first of three scores for the Leopards (6-1, 2-0 Patriot League) in the second quarter.
Davis Rodriguez added two field goals, including a 42-yard kick with 3 seconds left in the first half for a 13-7 lead at the break.
Maurice White finished with 107 yards and a touchdown on 24 carries, and Layton had 106 yards on five catches for Lafayette.
The Leopards, who won their fifth straight, had 23 first downs and controlled possession for almost 15 more minutes than the Rams.
Fordham was led by John Skelton with 245 yards, two touchdowns and an interception on 29-of-45 passing.