The Stars improved to 6-1 in their last seven home games and 14-3-2 in their last 19 in Texas despite being outshot 42-18. Turco, Dallas' top goalie the past seven seasons, hadn't played in three games.
"I saw the puck pretty good," Turco said. "I was excited to get back in there. The guys played a good, solid game and we got the lead."
Alex Auld, who began the season as Turco's backup, had started six of the previous eight games as coach Marc Crawford was looking to ride the hot hand in pursuit of a playoff spot.
Crawford said Turco earned the start in Dallas' next game, Thursday night at Columbus. The Stars are 1-9-2 in their last 12 on the road.
"[Turco] was huge," Crawford said. "That many shots, it's not the formula that we'd like. But I never felt we were out of control of the game."
Guillaume Latendresse's power-play deflection with 50 seconds left in the second period narrowed the deficit to 2-1, but Modano's one-timer from the right circle 25 seconds later restored Dallas' two-goal pad.
Andrew Brunette got the Wild within 3-2 with 3:57 left when he scored from in front, but Benn's goal from the right circle 53 seconds later extended the Stars' lead to 4-2.
Modano, the U.S.-born goal leader, moved into a tie with Johnny Bucyk for 23rd on the NHL career list.
Modano has scored seven of his 13 goals this season in the past 10 games in large part because Crawford has given the 39-year-old forward days off from practice.
"It's been a good stretch," said Modano, who added an assist and has 1,353 career points, tying Guy Lafleur for 24th. "I feel like I'm getting some good looks on net, and some quality chances and shots have been finding their way through legs and the goalies."
Backstrom and Harding had been the only goalies to play for the Wild since March 6, 2007, a streak of 234 games.
Dubielewicz was the winning goaltender in Houston's 3-1 victory over Abbotsford in the AHL on Monday night before joining the Wild on Tuesday.
"It's disappointing," Dubielewicz said. "I thought we put out a pretty good effort. We should have won this game. You double them in shots ... we battled hard enough where I had to come up with one more save, and I couldn't do it. That's pretty tough to swallow right now."
Dallas scored the only goal of the first period at 11:00 on Neal's deflection of Karlis Skrastins' shot.
Turco preserved the advantage with a strong first period as Minnesota held a 14-4 shots edge.
Richards' 50-foot slap shot beat Dubielewicz at 12:54 of the second period, 6 seconds after Dallas' 5-on-3 advantage had expired.
"I thought [Dubielewicz] could have been better," Minnesota coach Todd Richards said.
Despite being badly outshot, the Stars were able to respond quickly after the two Wild goals.
"They scored, but to go right back and force the issue and score was huge," Brad Richards said. "We did it twice tonight. That's probably why we won the game, those two shifts after those goals."
Modano entered the night tied with Mark Recchi for 24th on the NHL career goal list. ... Modano had his 92nd career game-winner, moving out of a tie with Wayne Gretzky and into a four-way tie for 10th with Jeremy Roenick, Teemu Selanne and Mark Messier. ... Minnesota's last win in Dallas was on March 21, 2003. ... Dallas C Brian Sutherby is out with a shoulder injury. ... Minnesota is without F Pierre-Marc Bouchard (concussion) and RW Chuck Kobasew (knee). ... Turco is 14-4-1 against the Wild. ... Dallas captain Brenden Morrow picked up his 1,000th career penalty minute with a second-period roughing call.