Rookie defenseman Matt Niskanen also scored for the Stars, who hadn't lost four in a row since a five-game skid in 2003. Mike Ribeiro, who signed a five-year, $25 million contract on Monday, added two assists.
Brenden Morrow also helped set up two goals for the Stars, 6-0-2 in their last eight home games against the Wild.
The Stars will begin a five-game trip Wednesday night at Chicago, and they didn't want to carry a long losing streak on the road.
"Having lost four in a row and going on a tough road trip, this was a must win," Morrow said. "We talked about keeping it simple and doing the things that made us successful. Tonight was a team game. We played as a pack."
The line of Miettinen, Ribeiro and Morrow got back on track after a four-game slump. The trio combined for 19 goals and 23 assists while Dallas was winning eight of nine before the slide.
"The main thing is that we worked harder, cut down on turnovers and did the things we know we can do," Miettinen said. "We focused on our strengths as a team. Hopefully we can build on this."
Mark Parrish scored Minnesota's goal. It was his 12th of the season and extended his goal streak to four games.
The Stars and Wild have seen quite a bit of each other lately, meeting for the third time in 13 days. The teams split the first two, with Dallas winning 8-3 at home. The Wild won 6-3 in St. Paul.
"Turco played very well and made some key saves for us," Stars coach Dave Tippett said. "We were trying to stop the bleeding. We had enough positives to push us through and work our way to a victory."
Niskanen helped Dallas take a 1-0 lead when he fired a loose puck past goalie Niklas Backstrom from low in the left circle at 5:50 of the second period.
That ended Dallas' scoreless streak of 107 minutes, 29 seconds. The Stars had been shut out in their previous two games, with Niskanen notching their previous goal last Thursday at Minnesota.
The Wild thought they'd tied it at 1 when Brent Burns knocked the puck past Turco at 7:36 of the second period. The goal was disallowed, however, because Turco bumped the net off its moorings a split-second before Burns' shot.
Minnesota scored the tying goal at 9:19 of the second period on Parrish's deflection four seconds after a Wild power play had expired.
Miettinen put Dallas back in front at 11:06 of the second on a slap shot from the top of the right circle that eluded a screened Backstrom. Miettinen made it 3-1 with his ninth goal of the season at 2:11 of the third period.
The only other two-goal game of Miettinen's career was on Dec. 29, 2006, against Nashville.
Minnesota coach Jacques Lemaire felt Dallas picked up the tempo midway through the second period.
"I thought they elevated their play," Lemaire said. "We didn't do enough offensively."
The Wild has lost three of four, but Lemaire thinks a timely goal or save could turn things around.
"We can't ask the goalie to do it all, but when games are tight, you need a huge save to keep you in the game," Lemaire said. "We've got to play a little better, maybe get a goal from a defenseman or a big save at the right time. We need a little help."
Ribeiro failed to score on a penalty shot at 11:44 of the first period. Ribeiro was hooked to the ice by Burns on a breakaway and was awarded the penalty shot, but his attempt was poke-checked away by Backstrom.
The Stars remain without three key players: RW Jere Lehtinen (abdominal injury), D Philippe Boucher (shoulder) and LW Jussi Jokinen (leg). ... Minnesota C Mikko Koivu, who missed his 23rd game due to a broken leg, has been practicing with the team. ... LW Derek Boogaard (back) is also out for the Wild. ... Ribeiro was set to become a free agent after the season, but after he scored a career high 21 goals through 40 games the Stars signed him to a long-term deal. ... The Stars, who've failed to connect on their last 23 power plays, were unable to capitalize on two 5-on-3 advantages.