Martin's wrist shot with 6:26 remaining in the final frame went in past a screened Ben Bishop and broke a 2-2 tie.
Andrew McDonald padded the winning margin with an empty-netter as the Islanders -- who came into the game holding the eighth and final Eastern Conference playoff seed -- collected their third win in four contests.
Evgeni Nabokov turned aside 19-of-21 for the Islanders.
Matt Carle supplied a goal and an assist, while Richard Panik also scored for the Lightning.
Bishop finished with 24 saves.
Millions of Getty images now available for free via embed tool
Aaron Carter is still in love with Hilary Duff