In the extra session, Eriksson picked up the loose puck in his own end, flew down the right wing and from the low circle wristed a puck high over Martin Brodeur for the win.
Eriksson also scored in regulation, Brad Richards had a goal and an assist while Brenden Morrow had the other goal for the Stars, who missed the playoffs last season for the second straight time. Kari Lehtonen stopped 27 shots in the win.
The Stars played their first game since 1989 without Mike Modano on the roster. The all-time leader in points and goals amongst American-born players signed with Detroit in the offseason.
Travis Zajac had a goal and an assist while Zach Parise and Jason Arnott each scored a goal for the Devils, who won the Atlantic Division last season, but were defeated by Philadelphia in the first round.
Martin Brodeur stopped 24 shots in the loss for New Jersey, which failed to win in the coaching debut of John MacLean, who was named coach of the Devils in the offseason after the team fired Jacques Lemaire.
Ilya Kovalchuk, who signed a much-publicized 15-year deal for $100 million in the offseason, finished the game with two assists. Kovalchuk’s initial contract with the Devils was voided by the league for attempting to circumvent the salary cap, and they were forced to re-work the deal to abide by league rules.
New Jersey took a 1-0 lead 2:45 into the game as Zajac, skating along the right slot, slid a soft shot between the pads of Lehtonen.
About 4 1/2 minutes later, the Devils made it a 2-0 game as Kovalchuk picked up the puck in the neutral zone after a Stars player fell down at the point, skated down the right wing on a 2-on-1 and dished the puck to Parise, who wristed it home.
Dallas, though, got one back four minutes later as Mike Ribeiro sent a pass on the fly from the left to the right circle where Morrow one-timed the puck past Brodeur.
The Stars tied the game 3:02 into the second thanks to a goal from Eriksson.
The Devils regained the lead on the power play as Patrik Elias skated behind the net to the right side and banked the puck off the boards for Arnott, whose one-timer from the top of the right circle got past Lehtonen at 10:22 of the second.
The Stars answered just 1:16 later when James Neal stole the puck deep and centered it for Richards, whose one-timer snuck past Brodeur.