Tristan Jarry made 24 saves for his first shutout of the season, Teddy Blueger had two goals and an assist, and Jake Guentzel had a goal and an assist for Pittsburgh (6-6-4), which ended a three-game losing streak.
"I thought we did a good job of moving our feet, putting pressure on them and getting some early goals to get the lead," Crosby said.
Cayden Primeau allowed five goals on 31 shots in two periods before he was pulled for Montreal (4-13-2), which has lost four straight. Sam Montembeault made 11 saves in relief.
"We have a lot of games and a lot of road to go," Canadiens defenseman Ben Chiarot said. "We have a game a day from now, so park this one and get ready for the next one."
Crosby, who had one assist through his first three games, put the Penguins up 1-0 when he drove to the net to finish off a three-way passing play with Guentzel and Bryan Rust at 3:36 of the first period.
"I was just trying to get up in the play, if a pass got broken up or if a puck laid there I was just going to try to clean it up, and 'Guentz' made a great play," Crosby said. "'Rusty' to 'Guentz,' and then 'Guentz' made a great play to find me there. I had an open net."
Crosby made his season debut in a 4-2 loss to the New Jersey Devils on Oct. 30 after having wrist surgery Sept. 8. The center returned from missing five games while in NHL COVID-19 protocol in a 6-1 loss to the Washington Capitals on Sunday and got his first point with an assist in a 3-2 loss to the Buffalo Sabres on Tuesday.
"He didn't have the preseason, no training camp, gets hit with COVID right away," Pittsburgh defenseman Kris Letang said. "Just COVID itself, when you're 10 days at home doing nothing, even if you can ride the bike it's nothing like going on the ice. It's a different type of conditioning, so it takes time. He's just going to get better and better. It's just a question of time."