Alexander Killorn and Martin St. Louis each tallied and provided a helper for the Lightning, who won for the first time since Feb. 23.
Anders Lindback turned aside 25 shots in the victory.
Keith Kinkaid stopped 12-of-13 shots in his first NHL debut after replacing the ineffective Johan Hedberg, but it wasn't enough to prevent the Devils' sixth straight loss.
Patrik Elias and Adam Henrique each scored for New Jersey.
Notable deaths of 2014 [PHOTOS]