Trailing 2-1 late in regulation, the Panthers tied it up with 27 seconds remaining when Shawn Matthias recorded his second goal of the game.
Jacob Markstrom compiled 24 saves as Florida won a second consecutive home game.
The Devils, who hold the seventh playoff seed in the Eastern Conference, dropped a third straight as Brodeur finished with 27 saves.
Steve Bernier scored both New Jersey goals.
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