Adam Lowry, Kyle Connor and Tyler Myers also scored for Winnipeg, who returned to the win column after being shutout 4-0 in Pittsburgh Friday night.
Jacob Trouba had a pair of assists for Winnipeg.
Alex Radulov scored for Dallas.
Ben Bishop turned aside 25 shots for the Stars, who lost for the first time in regulation in their last six games.
After a scoreless first period Dallas scored the first goal of the game on the power play just under two minutes into the second.
With Adam Lowry off for goaltender interference had a point shot from John Klingberg go in off of his skate as he was screening Winnipeg goaltender Connor Hellebuyck at at 1:56.
Lowry tied the contest a minute later after his initial shot was stopped after a nifty feed from the corner by Matthieu Perreault.
The Jet centreman snapped up the rebound before pivoting and beating Bishop high blocker side with a wrister to make it 1-1.
The goal was his 7th of the season.
Tyler Myers scored on a wraparound late in the second to give the Jets the lead after taking a Patrik Laine feed before working his way around the back of the Dallas net before tucking the puck in behind Bishop to make it 2-1.
"I don’t know if I’ve ever had a wraparound. But got one tonight," said Myers. "Yeah, you never really think of it like that. But it’s always nice to get a little bit of room. When something like that happens, the best thing to do is get the puck to the net somehow. And good things happen." Kyle Connor gave the Jets a two-goal cushion 1:15 into the third, firing a wrister from the high slot past Bishop through a screen provided by a leaping Blake Wheeler to make it 3-1.
The goal was his 14th of the season and snapped a 10 game pointless streak for the Jet forward.
"Yeah, felt good. Nothing’s really changed too much from my game. I thought I was a little quicker tonight, played with lots of speed," said Connor. "I’m not going to sit back and be happy. It’s the same approach, I’m going to come to the rink every day with a sense of urgency and keep trying to improve."
Josh Morrissey added a shorthanded empty netter with 3:30 left in regulation to clinch the win for the Jets.
Bryan Little scored a power play marker with 17.3 seconds left in the third period to make it 5-1 Jets.
Stars Head Coach Jim Montgomery felt his club played a solid road game.
"I thought we played a good road game. They make one play more than us in the first two periods and then we block a shot and it goes right to Connor and he makes a great shot to make it 3-1. Then we're chasing the game. I liked the way we continued to compete, we had some chances but we weren't able to get close."
Jets Head Coach Paul Maurice echoed that sentiment.
"I didn’t think that it’s a 5-1 game; almost, if it makes any sense, I would have preferred it finished 2-1 or 3-1 because that’s what it felt like from the bench. Real good in the first, especially in our own end; lots of hard battles. They’re an excellent second-period team. They really tried to stretch the game; we lost our forecheck at that time and then came back to it for the 3-1 goal. A great example of back on the forecheck and back in the offensive zone."
Both teams are back in action on Tuesday with divisional games.
Dallas visits St. Louis while Winnipeg hosts Colorado.
SHOTS-DALLAS 27 WINNIPEG 30