Dennis Wideman and Evgeny Dadonov scored power-play goals for Florida, which entered with the league's worst (10.3 percent) power-play unit. Scott Clemmensen made his second straight start and stopped 33 of 35 shots.
"We talked about having a fresh start the second half of the season with the power play and with some other areas of our game, and not dragging the first-half baggage into the second half," Panthers coach Pete DeBoer said.
Clemmensen improved to 3-0 lifetime against his former team with a 1.96 goals-against average.
"It's always nice to win, a lot of those guys are friends of mine. It's kind of like beating a big brother," Clemmensen said.
Nick Palmieri and David Clarkson scored for New Jersey. Brodeur had 19 saves as the Devils failed in their attempt to win a third straight game for the first time since a five-game winning streak from Dec. 12-21, 2009.
Still, New Jersey coach Jacques Lemaire was content with his team's two-game trip to Florida.
"Two good teams, and it's good to get three of four points," said Lemaire, whose team won 5-2 at Tampa Bay on Friday night.
The Panthers have won the first three games of a six-game homestand and improved to 6-2 in overtime.
Kulikov took a pass from Stephen Weiss, held the puck and skated in close, then fired the puck past Brodeur for his fourth goal of the season.
"That's just Russian finesse. Every other D-man would have just shot it," Wideman said.
"I saw it when it was behind me in the net -- I never saw it," Brodeur said. "When Kulikov walked in, he had so much time ... I just stayed there. Hopefully it was going to hit me, but he had the whole net to shoot at."
Clarkson tied the score at 2 when he jammed the puck past Clemmensen at 8:47 of the third period. Clemmensen sent the puck around the boards behind the net. New Jersey's Tim Sestito stopped it in the left corner and it bounced to Clarkson. The goalie extended his leg to stop Clarkson's first attempt but failed to stop the right wing's second try.
Wideman's power-play goal gave Florida a 2-1 lead 2:15 into the second period.
With Brian Rolston off for slashing, Mike Santorelli had the puck against the left board with the Devils overloaded to his side. He sent a cross-ice pass to Wideman, who wristed a shot past Brodeur for his fifth goal.
The score was tied at 1 after the first period.
Palmieri put home the rebound of Travis Zajac's shot to give New Jersey a 1-0 lead at 5:01.
Zajac won a left-circle faceoff and sent the puck back to Anssi Salmela. Zajac skated across the high crease and took a pass from Zajac before firing a shot at Clemmensen. Palmieri fought off Jason Garrison to put in the rebound for his second goal.
Dadonov evened the score on a power play at 15:07, when he wristed a shot to Brodeur's high stick side.
Wideman skated the puck into the Devils zone before passing to Weiss down the right side. Weiss made a drop-back pass to Dadonov, who skated around Sestito before putting it past Brodeur for his fourth goal. Only 3 seconds remained on Henrik Tallinder's tripping penalty.
Clemmensen has started three of four games in place of Tomas Vokoun. ... Santorelli has a five-game points streak. ... It was the first of four meetings between the teams. ... The Devils were 0-for-4 on the power play. They entered with the 27th-ranked power-play unit.
Copyright by STATS LLC and The Associated Press
Arena: BB&T Center Location: Sunrise, Florida
Referees: Brad Meier, Kevin Pollock Linesmen: Thor Nelson, Mark Shewchyk
Attendance: 17,825 (92.6% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Nick Palmieri (2)
Assists: Travis Zajac, Anssi Salmela
Evgeni Dadonov (4)
(Power Play) Assists: Stephen Weiss, Dennis Wideman
Dennis Wideman (5)
(Power Play) Assists: Mike Santorelli, Dmitry Kulikov
David Clarkson (8)
Assist: Tim Sestito
Dmitry Kulikov (4)
Assists: Stephen Weiss, Cory Stillman