Darryl Sutter coached his second game for the Flames after returning to the team when Geoff Ward was fired March 4.
''We've made some progress in terms of how we wanted to play,'' Sutter said.
Monahan scored the 200th and 201st goals.
''That's pretty cool,'' the 26-year-old center said. ''It's special when you win and you have a milestone, so it's something I'll probably remember here for a little bit.''
Mikael Backlund also scored for Calgary. The Flames improved to 13-12-3, winning consecutive games for the first time in a month.
''We're a lot sharper right now,'' Monahan said. ''We're playing together. When you're playing faster and moving your feet, it's going to generate a lot more looks and I think that's what we're getting right now.''
Jeff Petry scored for Montreal, and Carey Price stopped 33 shots. The Canadiens are 12-8-7, going 3-3-3 since Dominique Ducharme took over for the fired Claude Julien.
''I believe the guys did everything they needed to do to be ready,'' Ducharme said. ''So I was I was a little bit surprised to see how we were just not moving our feet.''
The Flames won the opener 2-1 on Thursday night.
Canadiens: At Winnipeg on Monday and Wednesday nights.
Flames: Host Edmonton on Monday and Wednesday nights.
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