The Blackbirds (6-3) led 47-37 at halftime and extended their lead to 15, 58-43, with 15:11 left in the second half before a 22-11 run by the Leopards pulled them with four, 69-65, with 6:02 left to play.
Lafayette (4-7) cut its deficit to two, 82-80, on a layup by Tony Johnson with 12 seconds left, but three free throws from the Blackbirds and a missed 3 from Ryan Willen sealed the win for Long Island.
Jared Mintz scored 18 points and had seven rebounds for Lafayette, while Johnson and Jim Mower added 13 points apiece.
David Hicks scored 15 for the Blackbirds, who overcame 23 turnovers and only made two field goals in the final four minutes.
The loss snapped a three-game winning streak for Lafayette after starting the year 1-6.