DALLAS — The Minnesota Wild turned to their offense to extend their winning streak.

Zach Parise scored two goals and added an assist and the Wild’s win streak reached six games with a 7-4 victory over Dallas Stars on Monday.

Both of Parise’s goals came on bounces that barely made it over the goal line. Mikko Koivu, Matt Cullen and Kyle Brodziak each had a goal and assist for Minnesota, which won for the first time in Dallas since March 21, 2003, snapping a 16-game losing streak in Dallas (0-11-5).

“It was a hard game,” said Parise, who leads the team with 14 goals. “I think we’re overcoming some demons this year with some buildings that have been hard for this team. That’s a good thing for us, we’re playing with confidence.”

With the game tied 4-4 in the third period, the Wild killed off a four-minute Dallas power play and even got a short-handed goal from Brodziak for the game-winner at 12:38.

“It’s been big for us all year,” Brodziak said of the Wild’s penalty-killing unit, which entered the game ranked third in the NHL.

“We’ve got a lot of guys who are smart hockey players out there who are also very hard workers, and that’s what you need on the PK. We seem to find a way to get the job done.”

Dany Heatley added an insurance goal with 1:28 remaining and Pierre-Marc Bouchard added an empty-netter with 16 seconds left, giving the Wild a season-high seven goals.

“I love the way that we’re scoring goals,” Wild coach Mike Yeo said. “There’s skill involved, but it’s matching our identity.”

Niklas Backstrom, who is 14-3-1 in his past 18 games and coming off a 2-0 shutout of San Jose on Saturday, stopped 22 shots for the win.

“I was real impressed with our guys to stick with it,” Yeo said. “It felt like things were not bouncing our way, and even just given the history of everything in here, but they found a way to win.”

Jaromir Jagr, Alex Goligoski, Trevor Daley and Philip Larsen scored for the Stars, who were playing their first game since longtime captain Brenden Morrow was traded to Pittsburgh on Sunday.

Kari Lehtonen, making his 12th straight start, stopped 35 of 41 shots.

“I didn’t think it was his strongest game,” Stars coach Glen Gulutzan said of Lehtonen.

“He made some real good saves, but I thought he overplayed a couple things.

“But you give them that much rubber, traffic in front of him and those opportunities, your goalie is trying to bail you out all the time.”

The Wild battled back from three one-goal deficits, taking the lead at 14:22 of the second period when Cullen snapped a 3-3 tie with his fifth goal of the season.

Larsen got his second of the season at 7:02 of the final period to make it 4-4, when he trailed the play and received a pass from Reilly Smith in the high slot and his wrist shot bounced off the bottom of Backstrom’s glove and rolled in.

The Stars had a good opportunity to take control when a high-sticking penalty to Mike Rupp put them on the power play for four minutes with 7:42 remaining.

But it was the Wild that capitalized as Brodziak scored just 20 seconds later while short-handed. A Goligoski turnover at center ice sent Cal Clutterbuck the other way, and although Lehtonen got a glove on his wrist shot, Brodziak popped home the rebound for his sixth of the season.

“It was a turnover in the neutral zone, and he just flew up the ice with it,” Brodziak said of Clutterbuck. “He made a good shot, kept the puck in play and fortunately, I was there to get the rebound. A great play by him.”

“We had an opportunity to win, seven minutes left, four-minute power play and you think you’re in the driver’s seat,” Gulutzan said. “We made a pass, turned it over. He jumped and capitalized. It’s a lot of the story of our game tonight.”

Dallas was unable to mount much of an attack during the rest of their man advantage and the Wild put the game away on Heatley’s ninth goal with 1:28 remaining.

After another Stars turnover in their own zone, Clutterbuck had two point-blank shots in front stopped by Lehtonen, but Heatley managed to jam home the rebound.

Bouchard added an empty-netter at 19:44.

“Obviously not the result we wanted,” Dallas center Jamie Benn said. “We keep getting the lead and keep giving it away. We definitely have areas we need to clean up. Anytime you give up seven goals, it’s not very good.”

The Stars took a 1-0 lead on Goligoski’s first goal of the season. After Roy stripped Ryan Suter of the puck behind the net, he fed a pass out into the slot, where Goligoski ripped a one-timer past Backstrom at 5:31.

Minnesota tied it at 7:35 on Parise’s 13th of the season. Lehtonen made a nice pad save on Devin Setoguchi and was down when Parise’s rebound shot bounced off Lehtonen’s arm straight up in the air.

Parise swatted it out of midair and the puck hit the crossbar, ricocheted straight down in the crease before Parise managed to nudge it over the line while falling.

The Stars jumped back ahead with 2:13 left in the first, while on a power play, when Jagr struck for his team-leading 14th goal, firing a one-timer off a Loui Eriksson feed into a half-empty net.

Koivu tied it again for the Wild when his quick wrist shot from the high slot beat Lehtonen between the pads at 3:42 of the second period for his eighth goal.

Dallas took the lead again just 1:28 later when Daley received a pass from Eriksson and sent a wrist shot from the right faceoff circle past Backstrom for his fourth goal of the season — and third in the past six games.

The Wild tied it again at 3 at 9:33. With Lehtonen having slid out to the right side of the crease, Koivu slid a pass from the right corner out front to Parise, who had been knocked onto his stomach but still swiped at it. The puck went off the right post and rolled along the goal line, as Daley tried to fish it out but ended up instead poking it over the line.

“You find yourself in some good spots, sometimes the goalie’s out of position, those are the fun ones,” Parise said. “I’ll take those.”

NOTES: Stars D Aaron Rome returned after missing 13 games with a foot injury. … Rupp, who sat out the previous three games with a lower body injury, was back in the lineup. … The Stars honored former D Darryl Sydor before the game for being a part of the club’s all-time 20th anniversary team. Sydor, now a Minnesota assistant coach, played in three different stints in Dallas between 1995 and 2009 and was part of the franchise’s Stanley Cup win in 1999.