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.
Celebrity Families of 2014 [PHOTOS]