Following a save by Devils goaltender Martin Brodeur on Carolina's Scott Walker, Madden cruised in on Hurricanes goaltender Cam Ward and put the puck through an open space between Ward's arm and body to end the game.
In the extra session, neither team was able to score.
Carolina kept the puck in the Devils' zone for nearly 1 1/2 minutes, but was unable to score in spite of five point-blank chances on Brodeur. New Jersey turned around in the final 20 seconds and fired two quick shots on Ward, who had to contort his body to stop each one.
Travis Zajac also scored in regulation, and four others recorded one point on the night. Brodeur picked up the win, making 26 saves for the Devils, winners in four of their last five games.