Dallas didn't score until Benn got his 25th goal with 3:13 left in the third. But Dubnyk stopped another shot by Benn from in front of the net with 1:00 left, after the Stars pulled goalie Antti Niemi for an extra skater. Minnesota's goalie had 15 saves in the third period.
"(Dubnyk) was solid all night," Wild coach Mike Yeo said. "He was real good at the end of the game too when he had to make a huge save with the goalie pulled. He was composed and he was calm in there all night and obviously made some huge saves."
Minnesota beat Dallas for the first time in four games this season. The Wild had lost the two most recent meetings despite taking leads of 3-0 and 2-0.
"That's not us as a group, those couple games where we allowed them back in the game," Dubnyk said. "You don't think back to those games. It's a completely new game."
Yeo had talked to the team about the late breakdowns against the Stars.
"There's been times this year where we've played solid hockey against them but when they've pushed, we didn't push back. In the third period, I know they got the goal there, but we could have had probably about four goals with so many opportunities that we had."
Dallas outshot the Wild 16-4 in the third period, but Niemi had to stop three close-in shots, two by Nino Neiderreiter. Niemi finished with 23 saves.
"To hold onto that lead, we played pretty simple hockey," Minnesota defenseman Jared Spurgeon said. "That's the way we need to play against a team like that."
"I think on a different night it will be a goal," Dallas coach Lindy Ruff said. "It was a tough one."
Dubnyk had no doubt the call was correct.
"He's got both feet in my crease. They kept showing the replay from behind that you can't see that his leg comes into my stick and my blocker, which doesn't allow me to make the save."
Yeo said when there's doubt, he will challenge calls.
"We'd rather get them wrong than miss one," he said.
The Western Conference-leading Stars have lost four of their past five games. Minnesota improved to 22-11-8 with 52 points — Dallas has 62 points.
In the first period, the Stars had 11 shots on goal to the Wild's six and had another 21 shots blocked or off the mark. The Wild outshot Dallas 15-8 in the second.
Carter skated in from the left corner to knock in a loose puck in front of the net at 3:34.
The Wild increased the lead to 2-0 at 11:20 when Vanek tucked a backhand into the net for his 13th goal.
NOTES: Benn had gone four games without a point. He and Spurgeon both received stitches to close cuts. ... In 17 career games against Dallas, Vanek has 17 points (8 goals, 9 assists). In his previous 11 games overall this season, he had scored only an empty-net goal. ... Minnesota is 1 for 21 on the power play over the last 11 games, and the Stars are 2 for 18 over their last seven. ... D Mike Reilly, who played high school and college hockey in Minnesota, made his NHL debut for the Wild. ... Streaks ended: Dallas' five-game home winning streak and Stars LW Patrick Sharp's career-best 11-game point streak.