It was Galchenyuk's second straight two-goal game, his fourth in seven games, and sixth of the season. He has nine goals in his past seven games and 23 this season.
"He's hot, he's so hot, everything he's shooting is going in but it's a mindset, and it's always been," said Canadiens captain Max Pacioretty, who had a goal and an assist while playing on Galchenyuk's line. "It's more of a mindset than anything, and I really like his patience with the puck. And I think it's opened up a lot of opportunities for other players, and I really like that he's shooting the puck."
Ben Scrivens made 30 saves for Montreal (31-30-6), who ended a four-game losing streak.
Lehtonen made 24 saves, and Cody Eakin and Ales Hemsky each had a goal and an assist for Dallas (40-20-8), who moved one point ahead of the Chicago Blackhawks for first place in the Western Conference.
Eakin deflected defenseman Jason Demers' centering pass from behind the Montreal goal line in the right corner at 2:58 of the first period. It was Eakin's 12th goal of the season and his first in 11 games.