Ilya Kovalchuk, who earlier scored his 40th goal, answered Patrik Elias' shootout goal to send the tiebreaker into extra rounds. Hossa and Devils captain Jamie Langenbrunner both found the net in the fourth round, and no one else scored until Dupuis.
Arron Asham shot wide of Johan Hedberg to end it, denying the Devils' hopes of being alone atop the Atlantic Division. Instead they had to settle for a first-place tie with Pittsburgh.
John Madden put New Jersey ahead 3-2 at 8:45 of the third, but it didn't hold up. The Devils finished the season series 3-0-1 against the Thrashers.
Atlanta pressed for the winner in the final 91 seconds of overtime during a power play. Vitaly Vishnevski went off for tripping soon after officials missed a high-stick by Devils defenseman Colin White that bloodied Ken Klee's face.
The Thrashers held a 5-1 shots advantage in overtime and peppered Brodeur, who was sharp - making a brilliant pad save on Slava Kozlov on the doorstep. Madden had several chances to clear the puck but couldn't get it out.
Brodeur, in his 17th straight start, made 29 saves before the shootout, and Hedberg stopped 30.
Zach Parise and Brian Gionta also scored for New Jersey.
Kovalchuk and Todd White had second-period goals to erase the Devils' 2-0 lead.