Tampa Bay put the game away in the second period on the goals by St. Louis and Killorn.
St. Louis' sixth tally of the season came on a 3-on-2 play that Killorn started in his own end. He made a pass to Lecavalier coming out of the Lightning's own zone, took a return pass in New Jersey's zone and then found St. Louis alone at the left side of the net for a tap-in at 5:33.
Killorn, who has four goals and four assists in 13 games since being called up, made a great play on the third goal. He skated out from behind the Devils' net, moved between the circles and beat Hedberg between the pads with Hedberg distracted by Lecavalier and St. Louis standing on either side of him.
Thompson upped the margin to 4-0 with a snap shot from in close after another nice set up by Conacher.
Henrique ended Lindback's bid for his first shutout of the season with a short-handed goal with 6:16 to play. Elias scored on a power play with 4:45 to go and Andrei Loktionov had a shot roll along the goal line with 2:00 to go. Lindback created a little excitement with 1:27 firing a shot at an empty net just wide.
B.J. Crombeen iced the game seconds later with an empty-net goal.
"I've been saying that we needed to work hard for a long time and tonight the hard work paid off," Lightning coach Guy Boucher said. "We played great against great opponents, but can't finish. We're right there with them and can't get it done. So many times, being good offensively is important. I told the players before the game that now is the time. They had to turn it up. They deserve this. I was hoping that a game like this would have come earlier."
NOTES: Tough guys Krysofer Barch of the Devils and Pierre-Cedric Labrie did more dancing than fighting in their first-period tussle. Both still got 5 for fighting. ... Palat has two assists in two games since being called up from Syracuse on Monday. ... This was the second of three games between the teams this season. The final one will be in Florida on March 29. ... The Devils have given up the first goal in seven consecutive games. ... Killorn has points in six of the last 10 games.