Eriksson added an empty-netter with 40 seconds left to help the Stars end the New Jersey Devils' three-game winning streak, 4-2 on Wednesday night.
Dallas' special teams have struggled all season, with the Stars starting the night 27th in the league in penalty-kill percentage and 22nd in power-play percentage.
This time, the Stars got a pair of special-teams goals and killed three of four Devils power plays.
"It was big," said Dallas' Brad Richards, who had three assists. "We killed some penalties and we generated some good chances on the power play. Scoring shorthanded, it was about time. It gave us some momentum."
Landon Wilson added a goal for Dallas.
Marty Turco had 25 saves for the Stars, 5-1-1 in their last seven.
Turco made a skate save on Patrik Elias' breakaway with 3:05 left to preserve a 3-2 lead.
"I tried to squeeze it for dear life," Turco said. "I wasn't sure, but when I heard the crowd cheer I knew it was out. I was hoping it hit my foot and it did."
Turco also came up with a sliding stop 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.
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.
"It's been a lot of games without one," Eriksson said. "It was nice to finally get one. We got the two points that we needed and that's what we were looking for."
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.
But the Stars rallied with a two-goal second period behind an 18-2 edge in shots.
Wilson skated to the front of the net to convert Mike Ribeiro's centering pass at 5:39 of the second period, evening the score at 2, and Parrish notched the go-ahead goal 4:19 later.
"I'm disappointed in how we played tonight," Devils coach Brent Sutter said. "The second period was a lack of competitiveness and a lack of intensity. It was probably our worst period all season."
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.