Lafayette's Tyrone Perry was fouled with 2.8 seconds remaining but missed the first first free throw. He missed the second intentionally and got the rebound but wasn't close on a desperate final shot as he went out of bounds.
Justin Jaworski, who led the Leopards in scoring coming into the matchup with 18 points per game, scored only six (2 of 11).
There were 17 lead changes and eight ties in the game.
Navy plays Boston University on the road on Wednesday. Lafayette faces Army at home on Wednesday.