Ben Chiarot and Blake Wheeler added singles as the Jets moved to 43-19-10 on the season to solidify their hold on second place in the Central Division with 96 points.
Connor Hellebuyck posted the win for Winnipeg, turning aside 28 shots.
Ben Bishop and Kari Lehtonen combined to stop 20 shots for Dallas, who dropped to 38-27-8.
The Stars lost their fourth straight and clung to the final playoff spot in the Western Conference with 84 points.
Bishop started but was replaced by Lehtonen with 9:49 remaining in the first period after moving across his crease to make a save on Bryan Little.
Patrick Laine got Winnipeg on the board with less than a second remaining in the first period with a power play marker. With Jamie Benn off for tripping the Jets won the ensuing faceoff in the Stars end before a sprawling Blake Wheeler got the puck to Laine in the slot which the Finnish winger promptly hammered past Kari Lehtonen to put the Jets up 1-0.
The goal was his 42nd of the season and 19th power play marker.
Wheeler took over the NHL lead in assists on the play with 61 this season.
Mattias Janmark tied the contest 1:13 into the second period, converting a Radek Faksa feed past Winnipeg goaltender Connor Hellebuyck to make it 1-1.
The goal was his 18th of the season.
The Jets regained the lead just over a minute later when a Ben Chiarot slapper found it's way through a crowd and hit the net just inside the right goal post at 2:17.
Patrick Laine scored at 6:43 firing a wrister just inside the far post on Lehtonen after receiving a touch pass from Nikolaj Ehlers from the high slot on the rush.
The goal was his 43rd of the season.
Dallas pulled to within a goal on the power play at 17:13 when Jamie Benn moved in off the side boards and wired a wrister which he managed to fit just under the cross bar over Hellebuyck's shoulder to make it 3-2.
The goal was his 26th of the season.
“I think we took a step in the right direction here," said Stars defenceman Jon Klingberg, who assisted on Benn's goal. "We played a better game five-on-five, we got one on the power play as well. Tough break on the (penalty kill) in the first, but that's how hockey is and we've just got to move on.”
Blake Wheeler added an empty netter with 1:29 left in regulation to make it 4-2 Winnipeg.
The goal was his 19th of the season.
“I thought we were resilient," said Wheeler. "They came out with a little bit of a push in the second, we answered right away, scored a big goal to get that lead again. It’s the way it’s going to be, 3-2 going into the third against a really good team. We had some really good moments in the third, they had some really good moments. Our goalie made some really big saves, so did theirs. So, it was a good hockey game. We did enough to stay out in front, and, like I said, scoring that goal pretty quick after they tied it was a big moment."
Stars Head Coach Ken Hitchcock was happy with the effort but not the result on the night.
"Winnipeg's got a good team. They make you pay for errors that you make in your own zone. We made a couple of them and they made us pay for it," he said.
"We did a good job. We did a really good job until they scored the flukey power play goal. I mean the guy is on his belly (Wheeler) and he makes a pass that goes through three people," said Hitchcock. "We did a really good job. But once he (Laine) gets a sniff you know that's what I told the players. You can't give him a sniff and we did a really good job until that last shift killing the penalty and he scored. That's all he needs."
SHOTS-DALLAS 30 WINNIPEG 24
NOTES-Jets D Jacob Trouba left the game early in the third period after colliding helmet-on-helmet before hitting the ice with his head. He will be evaluated Monday.
Dallas goaltender Ben Bishop is out for at least two weeks after leaving the game in the first period.