Josh Morrissey and Bryan Little each had a goal and an assist, and Adam Lowry, Tyler Myers, and Kyle Connor also scored for the Jets (26-13-2), who had lost three of their past four games and had scored one goal or fewer in four of their past five.
"I liked the way we played tonight, and if we can continue to build on this and play this way, this is where we want to be," Hellebuyck said.
WATCH: [All Stars vs. Jets highlights]
Alexander Radulov scored for the Stars (22-17-4), who have scored two goals or fewer in eight of their past 10 games. Ben Bishop made 25 saves.
"It wasn't a bad game," Bishop said. "I don't think the score reflected how we played. It's not the worst thing in the world, but obviously, you want to come away with some points."
Radulov gave Dallas a 1-0 lead on the power play, deflecting a point shot at 1:56 of the second period. Tyler Seguin got his 300th NHL assist on the goal.
"They had a really good start, especially the first four or five shifts they were rolling pretty good and had us on our heels," Little said. "It was one of those times that even though they opened the scoring, we were confident going into the rest of the game that we were going to come back."