Zach Parise scored the tying goal in regulation and had one of two New Jersey goals in the shootout to help the Devils beat the Lightning 3-2 on Thursday night.
Patrik Elias had the other Devils goal in the shootout, in which New Jersey outscored the Lightning 2-1.
Brian Rolston also scored in regulation for the Devils, who have won 14 of 17. New Jersey was coming off a 4-0 loss on Tuesday night at Florida.
"It was a good gut check for us," Rolston said.
Tampa Bay got two first-period goals from Ryan Malone. The Lightning have lost eight of 10.
Parise tied it at 2 on a rebound goal during a power play at 1:13 of the third. The left wing has 35 goals this season, including five over the past six games.
"After a loss, you want to respond the right way," New Jersey coach Brent Sutter said.
Malone put the Lightning ahead 1-0 when he wrapped a shot from the slot around Devils defenseman Mike Mottau and past goalie Kevin Weekes at 4:33 of the first. He made it 2-0 on a wrist shot from the top of the left circle with 7:05 left in the period.
"You don't like to give up leads at home," Tampa Bay center Jeff Halpern said. "It's frustrating. We did all right, but just not enough to win."
Rolston cut the Devils' deficit to 2-1 with a power-play goal at 2:16 of the second. His shot from just inside the blue line trickled past Tampa Bay goalie Karri Ramo into the net.
Weekes stopped Evgeny Artyukhin's shot on a breakaway midway through the third. He made 39 saves in regulation and overtime, and two more in the shootout.
"I thought especially the last two periods we really started creating some things offensively," Sutter said. "And after the second goal, Weeksey played extremely well."
The Devils finished with 40 shots.
Tampa Bay is 7-22 in games decided by one goal this season. The Lightning are just 11-6-6 when ahead after the first period.
"As a coaching staff, we have to be careful because if we see guys packing it in, then they won't be in the lineup," Tampa Bay interim coach Rick Tocchet said. "We have to go with people who are willing to stick to the system and want to play, and that's our job to make sure that happens."
Injured New Jersey G Martin Brodeur (left elbow) made the trip to Florida and watched the game from the Devils' booth in the press box. Brodeur, who last played on Nov. 1, has been practicing with the team. ... Tampa Bay defensemen Paul Ranger and Andrej Meszaros are scheduled to undergo left shoulder surgery on Mar. 3. Recovery time is expected to be within six months. ... Devils RW Brendan Shanahan returned after missing two games with a bruised right foot. ... Lightning LW Gary Roberts (maintenance) didn't play.