Chicago, which won seven straight from Jan. 20-Feb. 10, moved five points behind the Arizona Coyotes for the second wild card into the Stanley Cup Playoffs from the Western Conference. The Coyotes lost to the Edmonton Oilers 3-2 in overtime Saturday.
"I thought we played really well, and even though they were coming with pressure at the end, we didn't panic," Crawford said. "We kept things to the outside and then waited for pucks to come into the middle and break it out, so that was great by us not to lose our cool at the end."
WATCH: [All Blackhawks vs. Canadiens highlights]
Crawford, a Montreal native, got his second shutout of the season to win his fifth straight start. He is 9-2-2 with two shutouts in 13 games against the Canadiens.
His 48 saves tied the most by a Blackhawks goalie in a shutout set by Dave Dryden in a 3-0 win at the Philadelphia Flyers on Feb. 15, 1969.
"He was excellent," Blackhawks coach Jeremy Colliton said. "That's what he can do, and obviously it is in Montreal and he's pretty comfortable here, had a lot of success here, so he had a lot of confidence and it gives the team a lot of confidence that he's going to come through for us."
Connor Murphy and Brendan Perlini scored, and Alex DeBrincat had two assists for the Blackhawks (32-30-9), who went 1-4-0 in the five games that preceded their second-longest winning streak of the season.
"[Crawford] was unbelievable," Murphy said. "A couple of those saves, even in tight, they had a rebound right in front of them and it seemed like he almost tracked it into his glove, it was that good. And some of those saves seemed impossible, but that's why we're happy to have him."
Carey Price made 22 saves for the Canadiens (37-28-7), who have lost four of five and are 6-10-1 in the past 17 games.
"I thought we played very well," Price said. "I thought we definitely gave it a great effort and obviously Crawford played very well."
Montreal is three points behind the Columbus Blue Jackets for the second wild card from the Eastern Conference. The Blue Jackets lost 2-1 in overtime at the Boston Bruins on Saturday.
"Our backs are against the wall so we've got to win games, got to find a way to win," Canadiens defenseman Shea Weber said.
Murphy made it 1-0 with his fourth goal at 3:04 of the second period. He drove the slot and scored on a wrist shot after receiving Dylan Strome's pass off his left skate.