Tyler Toffoli scored shorthanded for Montreal, the No. 4 seed in the Scotia North Division. The Canadiens have won five straight games since facing elimination by the Toronto Maple Leafs in the best-of-7 first round.
"It was a difficult time and a challenge for us being down 1-3, but we believed that with what we went through, what we needed to make a push to come back in that round," Montreal coach Dominique Ducharme said. "And I think everyone engaging and stepping up their game and doing it together, and then at the same time we're learning to win as a group."
Connor Hellebuyck made 23 saves for the Jets, the No. 3 seed, who were shut out for the first time this postseason.
Teams that take a 2-0 lead on the road are 82-20 (80.4 percent) winning a best-of-7 playoff series, including 2-0 this season. Game 3 is at Montreal on Sunday (6 p.m. ET; NBCSN, SN, TVAS).
"Big improvement for us from Game 1 (a 5-3 loss on Wednesday)," Winnipeg coach Paul Maurice said. "Neither team scores an even-strength goal, hard-to-come-by opportunities at either end of the ice. But much, much better than our Game 1."
Toffoli scored the only goal of the game on a 2-on-1 with Artturi Lehkonen at 1:41 of the second period to give Montreal a 1-0 lead.
The Canadiens have scored first in five straight playoff games for the first time since 1993, when they scored first in six in a row and won the Stanley Cup.
"I think when we had our backs against the wall (against Toronto), I think we all looked at ourselves in the mirror and I think we all saw that we had much better," Montreal forward Phillip Danault said. "This couldn't be it. It couldn't be like that, our year. We've went through a lot and we've got a tight group. Good energy in the locker room."
Price made 14 saves in the third period, including against Kyle Connor with three seconds left.
"They put the pressure on," Price said. "Obviously, they're playing desperate hockey at the end of the game and they're just funneling pucks towards the net. Like I said, we battle and compete in front and some of them just hit you."
The Jets were without center Mark Scheifele, who served the first of a four-game suspension he received for charging Canadiens forward Jake Evans in Game 1. Scheifele led Winnipeg in the regular season with 63 points (21 goals, 42 assists) in 56 games and had two goals and three assists in five playoff games.
"Aside from not scoring, we played a full 60 (minutes) today," Winnipeg forward Nikolaj Ehlers said. "We played hard and we've got to keep that going. We work hard for each other, it's going to go well. We're going to take a look at this game and look forward to the next one."
NOTES: It was Price's eighth NHL playoff shutout, fifth on the road. … The Canadiens are the third road team this postseason to win Games 1 and 2, joining the Jets (Edmonton Oilers) and the Tampa Bay Lightning (Florida Panthers, Carolina Hurricanes). … Lehkonen replaced Evans and had one assist, one hit and two blocked shots in 15:49 of ice time in his first game since May 24. … Jets center Paul Stastny missed his second straight game because of an undisclosed injury. Scheifele and Stastny were replaced by forwards Kristian Vesalainen (one shot, three hits in 13:50) and Jansen Harkins (three hits in 7:47).
