Marty Turco made 25 saves for the Stars, 5-1-1 in their last seven.
Turco stopped Patrik Elias on a breakaway with 3:05 left and made a sliding save on Devils top scorer Zach Parise's shot from the left circle with about 14 minutes remaining to preserve the 3-2 lead. Parise had three goals in his previous two games.
Dallas started the night 27th in the league in penalty-kill percentage and 22nd in power-play percentage.
David Clarkson had a power-play goal, and Mike Mottau also scored for the Devils, who had been 5-1-1 in their last seven on the road and were coming off Tuesday night's 4-3 win at St. Louis.
Scott Clemmensen stopped 40 shots for the Devils.
With the game tied at 2, Parrish's rebound at 9:58 of the second period put Dallas ahead for good.
Eriksson took a lead pass from Trevor Daley and scored his 19th of the season from the right circle while the Stars were on the penalty kill for the game's first goal at 10:09 of the first period.
Mottau notched his first goal of the season from the high slot through Turco's pads to tie it at 1 at 17:30 of the opening period.
Dallas' Stephane Robidas was in the penalty box for hooking when Clarkson's rebound gave New Jersey a 2-1 advantage with 24 seconds left in the first period.
The Stars rallied with a pair of goals in the second period behind an 18-2 edge in shots. Wilson set up in front of the net to convert Mike Ribeiro's centering pass at 5:39 of the second period, evening the score at 2.
Notes: The Stars called up Ivan Visnevskiy from Peoria of the AHL earlier in the day. The 20-year-old defenseman, Dallas' first-round pick in 2006, was among the Stars' scratches. ... Dallas lost the only other meeting between the teams this season, 5-0 on Oct. 22 in New Jersey. ... Devils top goalie Martin Brodeur is working out off ice as his rehab continues from surgery two months ago to reattach a torn tendon in his left arm. Brodeur is on schedule to return in February. ... New Jersey D Colin White is out with an upper-body injury. ... Parrish has 15 goals in 37 games against the Devils.
... The Stars had lost three straight in their annual home game on New Year's Eve.
