Mattias Janmark, Jason Dickinson, Radek Faksa, Jamie Benn and Tyler Seguin scored, Corey Perry had three assists, and Ben Bishop made 23 saves for the Stars (13-8-2), who are 12-1-1 in their past 14 games and have a 10-game point streak (9-0-1) after starting the season 1-7-1.
"Confidence," Perry said. "I think if you look around the room, everybody is playing with confidence. Everybody wants the puck. Everybody's holding onto the puck and is making strong plays. If you keep doing that in this league, you're going to have success."
[WATCH: All Jets vs. Stars highlights]
Kyle Connor, Patrik Laine and Luca Sbisa scored, and Connor Hellebuyck made 31 saves for the Jets (13-9-1), who rallied to tie the game after falling behind by three goals but lost for the first time in four games.
"[We] haven't quit in a game all year," Winnipeg coach Paul Maurice said. "It doesn't always go the way you want it to go, but I'm really proud of that. I don't think it was easy for us tonight in terms of execution, and we had a few miles on us."
Video: WPG@DAL: Janmark jumps on rebound and scores
Hellebuyck made 13 saves and Bishop 10 in the first period, when neither team scored.
Janmark scored on a rebound at 7:37 of the second period to give the Stars a 1-0 lead. It was his first game back after missing the previous four with a lower-body injury.
"He's got some speed," Perry said of Janmark. "He's a smart player. The goal he scored, he found a way to get backdoor and get lost. Good players do that."
Dickinson scored by deflecting a Taylor Fedun shot at 9:43 to make it 2-0. Maurice challenged for offside, but the goal was upheld after video review, and the Jets were assessed a delay of game penalty.
"We had one there in the third period where [Dmitry Kulikov] made the same play, and they called it offsides," Winnipeg captain Blake Wheeler said. "We seemingly challenge every goal and even when you watch it in slo-mo for as long as you can … I don't know."
Faksa scored at 13:19 to give the Stars a 3-0 lead. He has four goals and five assists during an NHL career-high eight-game point streak.
"I think Radek is playing to his strengths," Dallas coach Jim Montgomery said. "He's getting on top of pucks in the offensive zone, he's putting people on his back, he's getting to the scoring areas, and he's owning the net front. That's the strength of his game."
Connor scored 39 seconds later on a turnover to make it 3-1.
Perry had an assist on each of the three Stars goals in the second.
Laine scored when the puck went in off his chest at 8:35 to make it 3-2.
Sbisa scored on a shot from the slot at 15:14 to tie the game 3-3. It was his first NHL goal since Feb. 21, 2018, when he was with the Vegas Golden Knights.
"It's been a little while for myself," Sbisa said. "It came at a good time. But at the end of the day, it doesn't really matter. All we came here for was the two points."
Benn scored on a backhand shot in front of the net at 15:39 to give the Stars the 4-3 lead. The Dallas captain has the game-winning goal in three straight games. He had five shots on goal in the third period.
"He was all over the puck," Montgomery said. "He had the big hit, and I think he was refusing to let us lose."
Seguin scored into an empty net with 34 seconds remaining to make it 5-3. The goal was upheld after video review on a challenge for offside initiated by the Situation Room.
Video: WPG@DAL: Dickinson tips in gorgeous top-shelf goal
They said it
"It was outstanding. I think our best game on effort was Nashville, and execution was Florida. I liked our heart in here tonight, but probably not our execution so much. But when you come off a 10-day trip, go home, and go back out for a long one again, you want the heart to be there first." -- Jets coach Paul Maurice on a 3-1-0 road trip
"I think you saw right off the face-off, he jumped from his coverage and he was hunting the puck. You could see that he was out there to score a goal and that's what he's done throughout the years when he's been at his best. I thought about it from the face-off that, 'Okay, now he's out there to do some damage.' I think when our team is at our best, that's how we see him." -- Stars forward Mattias Janmark on Jamie Benn's game-winning goal
Need to know
Laine has five points (two goals, three assists) in the past four games. … Benn has seven points (four goals, three assists) during a four-game point streak. … Perry has back-to-back multipoint games (one goal, four assists).
Jets: Host the Columbus Blue Jackets on Saturday (7 p.m. ET; SN360, SNW, FS-O, NHL.TV)
Stars: Host the Chicago Blackhawks on Saturday (8 p.m. ET; FS-SW, NBCSCH, NHL.TV)
Video: Benn's late goal pushes Stars past Jets, 5-3