Gaudreau extended his point streak to seven games when he scored from the right face-off circle to put Calgary up 1-0. He handled a flip pass from the left side with his left glove and dropped it to the ice before scoring on a wrist shot over Allen's left shoulder.
"It's definitely important to get the lead," Flames forward Matthew Tkachuk said. "We haven't played with the lead a whole lot in the last couple of weeks, so it was definitely nice to get the first one."
Backlund scored into an empty net to make it 2-0 with 32 seconds remaining.
"We knew they were going to come out hard at the beginning, which they did," Canadiens defenseman Ben Chiarot said. "And I thought their goalie played exceptional tonight."
Canadiens forward Josh Anderson did not finish the game after playing 6:06. Montreal coach Claude Julien said Anderson was sent home with flulike symptoms.
"Obviously we don't want that spreading, but he's tested negative for COVID testing," Julien said. "He'll be tested again tomorrow, but with everything that's going on right now it was cautionary measures by our medical staff to send him home."
NOTES: Gaudreau has scored nine points (five goals, four assists). His streak is the longest by a Flames player to start a season since 2013-14, when Jiri Hudler scored 12 points (four goals, eight assists) in the first nine games. ... Giordano, a defenseman, played his 900th NHL game, all with Calgary.