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.
