The Lightning had it after losing five games in a row and the Devils didn't seem to find until they fell behind by four goals in seeing their winless streak stretch to six games.
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"We really needed this one," said Thompson, who also had an assist on the Lightning's final goal. "We were desperate. We talked all day about doing the little things right. It always feels good when you can contribute. I don't get a chance to score two goals often. I was pretty close to a third. We did a great job of taking advantage of our opportunities. Both of my goals tonight came off great passes. I'd be a fool if I missed them.
"You get a win like this and it can give us momentum moving forward. We just needed to get it going, relax, and play our game."
"I never want to let a shutout go, but the win was more important," said Lindback, who has not had a shutout since 2010. "I can get a shutout another time. It was a huge game for us. We've been on a tough road trip and just been struggling. We showed all game that we're a better team than we have been playing."
New Jersey's slide has taken place with Johan Hedberg in goal for the injured Martin Brodeur (back). The crowd at the Prudential Center cheered wildly after coach Peter DeBoer sent Keith Kinkaid out for his first NHL action after Tampa Bay opened a 3-0 lead.
DeBoer refused to blame Hedberg got the slide and said he would be back in goal Thursday against Buffalo, even though he said Kinkaid played well, stopping 12 of 13 shots.
"We have to build off the last four minutes," DeBoer said. "This is our adversity. Every team faces them at different points in the year and this is ours. You hope that you get to the bottom here so you start climbing up. I'm hoping this is rock bottom and we can start getting off the mat and getting on to bigger and better things."
The only good thing the Devils did was end Steven Stamkos' 10-game point streak. He had scored goals in eight of his last nine games, and only a pad save by Kinkaid on a breakaway early in the third period prevented the streak from continuing.
"Seeing him come down, top goal scorer in the league, to get a stop on him, just a pad, he's a great player," Kinkaid said. "Maybe he roofs it, it's in, but I got a lucky pad on it."
Thompson put the Lightning ahead for good with 2:56 left in the first period. Hedberg played the puck from behind his own net and Lightning rookie Ondrej Palat got the puck in the corner, found Conacher in the left circle. The rookie found Thompson alone in front for a shot that Hedberg never had a chance to stop.
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."
- Tough guys Krysofer Barch of the Devils and Pierre-Cedric Labrie did more dancing than fighting in their first-period tussle. Both still got five 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 past 10 games.