The Jets, who were facing elimination, forced game 6 on Saturday in Dallas and now trail the series 3 games to 2.
"You know I think that we've been building our game all season long. It's unfortunate we've got into this position but you know what? I believe in this group, I believe in myself and I believe in all of our fans. We're going to continue to compete and you know leave it all out there," said Hellebuyck.
Though reluctant to talk about his second shutout of the series, Jets Captain Adam Lowry said Hellebuyck's key save early in the second to was something he is used to seeing.
"That was incredible," said Lowry. "I mean but that's what he's done for us all year. You know what? Another stellar game by him. But like you said, it's 0-0. We had a bit of a breakdown. Easily could be down 1-0 there. You know it gets the building on their feet. It gives us some energy and let's us take a deep breath...we have so much confidence in Connor and what he does and what he means for our team. Games like tonight are certainly the reason we got the win."
Mark Scheifele scored once and added an assist.
Vladislav Namestnikov scored the other Jet goals.
Kyle Connor and Neal Pionk each had a pair of assists.
Jake Oettinger turned aside 31 shots for Dallas, who The Jets carried the edge in play in a scoreless first period, outshooting the Stars 11-4.
Scheifele opened the scoring 6:17 into the second period on a line rush when his attempted pass to Connor was redirected by Stars defenceman Thomas Harley's skate into the net.
The goal was Scheifele's 4th of the playoffs.
With the Jets enjoying a two-man advantage early in the third, the Winnipeg power play took advantage when Mark Scheifele sent a cross ice pass to Kyle Connor who relayed it to Nikolaj Ehlers by the side of the Dallas net.
The veteran winger took a stride before sliding it past Oettinger to make it 2-0 Jets.
The goal was his 4th of the playoffs.
Vladislav Namestnikov got Winnipeg's third goal on the power play 12:07 into the third.
With Lian Bichsel off for roughing, Namestnikov converted an Alex Iafallo feed from behind the goal line, beating Oettinger just under the cross bar to make it 3-0 Winnipeg.
The goal was his 3rd of the playoffs.
Nikolaj Ehlers added an empty netter with 45 seconds left in regulation to seal the win for the Jets.
Jets Head Coach Scott Arniel thought it was a total team win.
"That was everybody. That was our whole roster stepping up, knowing what the challenge was and putting their best game on the ice and it was everybody stepping up not wanting to be eliminated tonight," he said. "You could see it right from the puck drop the opening shift and we didn't take our foot off the gas."
SHOTS-DALLAS 22 WINNIPEG 35
ATTENDANCE-15,225
