The Devils have won three straight road games to start the season and kept the Lightning from taking at least a point in all four games of a season-opening homestand.
Cammalleri's fourth goal of the season came on a power play. Lightning goalie Evgeni Nabokov stopped a Patrik Elias shot in front of the net but failed to cover the loose puck, allowing Cammalleri to score off the rebound.
Elias said it was a designed pass.
"I had one redirection from Marty [Havlat] and once I saw the puck pop out I tried to slide it to Mike," Elias said. "Why would I shoot it with the goalie right there?"
Cammalleri said, "It was a nice play by him. He's a very intelligent hockey player. When you play with him, you see that he sees the plays before they happen."
The Lightning tied the game 1-1, 8:59 into the third period when Alex Killorn scored his first goal of the season off an opportunity generated when Tyler Johnson split Bryce Salvador and Dainius Zubrus to provide the open look for Killorn.
"I thought we made a nice surge there in the third period but they came back and scored on the power play," Lightning defenseman Victor Hedman said. "It's a tough game to lose because we had a chance to get the two points and didn't make it happen."
Devils goalie Cory Schneider made 26 saves and did a good job controlling the puck and keeping the Lightning from getting the second and third chances that helped them score seven goals Monday against the Montreal Canadiens.
"They blocked a lot of shots tonight," Hedman said. "And we needed to make sure those shots went through."
The Lightning applied pressure on Schneider early in the first period and had a 7-0 shot advantage through the first five minutes. At 3:29, Nikita Kucherov thought he scored and raised his arms in celebration when his wraparound appeared to go past Schneider's pad. A video replay ruled the puck did not completely cross the line. From there the Devils appeared to get back on track defensively and slowed down the game.
"I thought we showed a lot of grit and determination," Devils coach Pete DeBoer said. "Schneider made some big saves early and that gave us a chance to get our legs going."
After the morning skate, DeBoer said the Devils wanted to place an emphasis on keeping the Lightning from generating multiple opportunities in the attack zone.
"We had a couple of breakdowns in the third period in the neutral zone more than the offensive zone, and they scored on one of them," Elias said. "After that we were solid, making the right plays, not panicking in our zone, and again [Schneider] made some big saves there."
"Our special teams really made the difference tonight because we had a couple of big penalty kills and eventually got the goal on the power play," DeBoer said. "They are a good team so we knew it was going to be a tight game and the guys just battled to get it done. It was just a good hockey game."
Stamkos was held to four shots, one night after scoring a hat trick on 12 shots.
"I thought we came out strong in the second and the shots got the post instead of the net," Stamkos said. "And we passed up some chances to shoot, which we can't do against a team that doesn't give you many quality chances."
The Devils took a 1-0 lead 7:38 into in the second period when Travis Zajac scored on a second-chance shot after his first bounced off Nabokov's glove.
"We are getting contributions from a lot of different areas right now," DeBoer said. "And that's what it takes to win games against good teams."
Nabokov, making his first start for the Lightning, made 23 saves.