The Lightning received a goal and an assist from Brayden Point, and Brandon Hagel and Steven Stamkos scored.
Victor Hedman posted two assists while Andrei Vasilevskiy stopped 28 shots but lost for the first time in five games.
Kyle Connor scored for the Jets, who lost for the third time in their past 11 games.
Matthew Tkachuk, who leads Florida with 24 goals, scored twice with the man advantage.
Colton Sissons and Mattias Ekholm scored for the Predators, whose two-game win streak came to an end.