Curley was 20-for-28 passing with 241 yards and an interception for the Leopards (3-1), while Layton caught seven balls for 116 yards. Maurice White finished with 131 yards rushing on 21 carries and a touchdown.
Lafayette answered with 24 straight points, highlighted by Curley's 17- and 4-yard touchdown passes to Layton to give the Leopards a 24-7 lead in the fourth quarter.
White sealed the scoring with a 6-yard TD run with 3:13 left.
Witt and Brook Hart threw one TD pass apiece for Yale.