The Devils, last in the overall standings, beat the Lightning for the second time in six days, riding a four-goal first period to a 5-2 victory on Friday night that snapped an 11-game road losing streak.
The road slide by the NHL's last-place team (12-29-2, 26 points) was one off the franchise record of 12, set from Oct. 19 to Dec. 1, 1983.
It's been a tough season for the Devils, who have already changed coaches and endured more regulation losses than they had all of last season. But Jacques Lemaire, who took over as coach on Dec. 23 when John MacLean was fired, thinks his team may be turning things around.
"A little bit," said Lemaire, who is now 3-7-0 since returning. "It's still early, but I think we're on the right track. I think the guys started to believe that if they work together, they'll have a better chance to score than working on their own."
It was the Devils' first win on the road since a 5-3 triumph in Chicago on Nov. 3 -- but the 12th in their last 14 meetings with Tampa Bay since the start of the 2007-08 season.
The best news for the Devils was the performance of goaltender Martin Brodeur, who made 30 saves and slammed the door after New Jersey gave him a 4-1 lead after one period.
"Marty was good when he had to be," Lemaire said. "Again, he gave us a chance to win because they had some good chances at different times and he was there to make the big save."
The Lightning, who allowed five third-period goals in a 6-3 loss at New Jersey on Monday, were coming off perhaps their best game of the season -- a 3-0 win against Washington on Wednesday. But after Steven Stamkos gave the Bolts an early lead with a power-play goal, the wheels came off -- the Devils scored four times in less than eight minutes and led 4-1 at the first intermission.
"It's unacceptable for us to get behind by that much," Stamkos said.
Ilya Kovalchuk tied it at 7:59, beating Dwayne Roloson from the high slot with a one-timer. Brian Rolston put the Devils ahead at 9:19, Patrik Elias scored at 11:44 and Travis Zajac ended Roloson's night with a shorthanded goal at 15:54.
Zajac's goal was New Jersey's League-low 80th of the season -- but nine of those came in less than 40 minutes in the back-to-back wins against the Lightning.
"When you give Jacques' team a lead, you're asking for trouble," Tampa Bay coach Guy Boucher said.
Martin St. Louis cut the deficit to 4-2 when he lifted a backhander over Brodeur during a breakaway with 5:05 left in the second. Stamkos assisted on St. Louis' goal for his 200th NHL point, coming in his 206th game.
But Kovalchuk ended any comeback hopes when he beat Roloson's replacement, Dan Smith, with 6:20 left in regulation.
Brodeur improved to 33-15-7 in 57 games against the Lightning. He has an NHL-record 609 regular-season wins -- but is just 7-18-1 this season, by far the worst of his career.
"He's had a rough go and he's taken a lot of heat, and he was awesome for us tonight," Rolston said.
Material from team media and wire services was used in this report