Hellebuyck's 22nd NHL shutout is the first by any Winnipeg team at Montreal.
"I think a shutout, no matter where it comes, is awesome, especially in this league," Hellebuyck said. "Most shutouts are a team shutout and tonight was no different. The guys are blocking shots and keeping them to the outside and letting me see the shots altogether and really applying the pressure in the O-zone. I thought we were a good team tonight."
Nikolaj Ehlers, Andrew Copp and Mathieu Perreault each had a goal and an assist for Winnipeg (25-13-3), which swept the two-game set to begin a five-game road trip. The Jets are 7-2-1 in their past 10, including a 4-2 win Thursday.
"I think the best part of the game was, for us, that we improved from our first game in here," Jets coach Paul Maurice said. "We had given up a fair amount off the rush. And we were much, much better at it. I also think we got stronger with it as the game went on. The areas that we thought we needed to improve from game one we did."
Jake Allen made 20 saves in his third start in four days for Montreal (17-12-9), which has lost each of the three games goalie Carey Price has missed because of a lower-body injury.
"I feel that tonight we came out a little bit on our heels, being scared of making those mistakes," Canadiens coach Dominique Ducharme said. "But being smart doesn't mean that you have to be passive. I thought we were a little passive. Yes, we were not giving much, but a little passive. Scoring a first goal in that kind of game probably would give energy to our guys, and getting scored on did the opposite, so I didn't like that reaction."
Paul Stastny gave Winnipeg a 1-0 lead at 10:13 of the second period. Allen raced from his crease to poke the puck away before Jets forward Pierre-Luc Dubois could reach it, but Canadiens defenseman Jeff Petry turned it over to Stastny, whose shot went in off Allen.