Madden whipped a forehand over Cam Ward's stick, sending the Devils to their fourth win in five games. Earlier in the shootout, Brian Gionta scored for New Jersey in the second round before Rod Brind'Amour countered for Carolina in the third.
The Devils got regulation goals from Travis Zajac and Jim Dowd as they beat the Hurricanes, who knocked New Jersey out of the 2006 playoffs in the second round, for the second time in two meetings this season. Dowd sent the game into overtime by scoring with 1 minute remaining.
Eric Staal and Brind'Amour scored for the defending Stanley Cup champions.
The Hurricanes outshot the Devils 8-7 in a scoreless first period. Carolina had the better chances early but New Jersey stepped up the pressure in the final five minutes of the period with Zach Parise and Zajac getting close-in chances.
The teams exchanged power-play goals in the second with New Jersey connecting first at 7:50 when Zajac knocked Parise's rebound past Ward.
The Hurricanes cashed in a golden opportunity when the Devils lost two defenceman to delay-of-game penalties for shooting the puck over the glass. Alex Brooks was whistled first, followed by Brad Lukowich 24 seconds later.
Stall converted the 5-on-3 advantage with a hard drive from the point at 9:39 to beat Martin Brodeur for his team-leading ninth goal.
In the third, Brind'Amour scored with 4:15 remaining to give the Hurricanes a 2-1 lead. Brind'Amour fired a shot from a sharp angle that Justin Williams appeared to deflect under Brodeur.
Dowd sent the game to overtime when he beat Ward from the slot with time running out. It was the first goal for the New Jersey native since rejoining the Devils as a free agent on Nov 2.
Brind'Amour and Williams each had two outstanding chances to win the game in overtime as the Hurricanes kept the puck in the Devils zone for more than a minute. Brodeur made several sprawling stops to send the game to a shootout. Carolina outshot New Jersey 5-2 in overtime.
Notes: RW Trevor Letowski returned for Carolina after missing nine games with a concussion. For New Jersey, Lukowich returned after four games with a bruised foot while C Scott Gomez remained sidelined with a groin pull. ... Brodeur has started 13 of the Devils' 14 games, including the last seven. ... The Hurricanes are 0-4-1 against teams they eliminated from the playoffs last year.