Calgary closed within four points of Montreal for the fourth and final playoff spot in the North Division.
''It's right there for us,'' 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.''
Milan Lucic, Brett Ritchie and Rasmus Andersson, with an empty-net goal, also scored and Jacob Markstrom made 30 saves to improve to 6-1 against Montreal this season. The Flames opened the three-game set Friday with a 3-2 victory.
Tyler Toffoli and Nick Suzuki scored for the Canadiens.
''It's frustrating knowing the situation we're in and the way we're playing,'' Montreal defenceman Jeff Petry said. ''We have to find a way to battle this out together.''
Cayden Primeau made 29 saves in his season debut and third career start for Montreal. He's the son of former NHL player Keith Primeau.
The teams will close the series Monday night in Calgary.
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