Tyler Toffoli scored his 25th goal of the season, and Akira Schmid made 23 saves in his first start since Dec. 21 for the Devils (29-25-4), who are 1-3-0 in their past four.
Coach Lindy Ruff was asked after the game if he feels responsible for New Jersey being in fourth place in the Metropolitan Division, five points behind the Philadelphia Flyers for third.
"I take full responsibility," Ruff said. "You want to win, and we've dealt with a lot. Players want to win. I'm responsible for the wins and losses, who gets on the ice and who doesn't get on the ice.
"I said this before, we've got a passionate fan base. They want to see wins, and if you look at our home record (14-15-2), that part hurts, so I feel fully responsible."
Hedman gave the Lightning a 1-0 lead on a shot from the bottom of the left face-off circle at 1:27 of the second period.
"Just get open and 'Kuch' will find you," Hedman said. "I was just kind of mirroring [Kucherov] all the way down just in case he needed me, and it came over."