Thomas Harley and Matt Duchene also scored for the Stars (9-3-1).
Scott Wedgewood made 31 saves in net for Dallas.
The loss snapped a three-game winning streak for the Jets.
Dallas had taken a 3-1 lead into the third period. The Stars scored their third goal of the second period on the power play. With Dillon off for tripping, Duchene scored from alone in front when he was set up by Johnston and Evgenii Dadonov just as Dillon’s penalty was about to expire.
Dallas took a 2-0 lead while shorthanded when Johnston stole the puck from Perfetti inside the Jets blue line, then fired a shot past a surprised Hellebuyck.
After a scoreless first period, the Stars pounced on Winnipeg early in the second. After a goal-mouth scramble, the puck came out to Harley, who fired the puck past Hellebuyck. Ryan Suter assisted.
Stars: Visit Minnesota on Sunday.
Jets: Host the New Jersey Devils on Tuesday.
AP NHL: https://www.apnews.com/hub/NHL
The Associated Press