Johnny Gaudreau scored twice, and Jacob Markstrom made 30 saves for the Flames (21-23-3), who defeated the Canadiens 4-2 here Friday.
Calgary moved four points behind Montreal for fourth place in the seven-team Scotia North Division. The top four teams qualify for the Stanley Cup Playoffs.
"Every game is important the remainder of the season here, especially against this team," Gaudreau said.
"If we take care of ourselves and we keep playing the way we've been playing the past few games, I think we've got a real good shot to make a push here."
Tyler Toffoli and Nick Suzuki scored for the Canadiens (20-17-9), who have lost four of five. Cayden Primeau made 29 saves in his first NHL start of the season and third of his career.
"Every time you lose a game it's frustrating," Montreal defenseman Jeff Petry said. "I can't tell you an exact number on a scale, but it is frustrating knowing the situation we're in and the way we're playing. We have to find a way to battle this out together."