They finally broke through on the scoreboard late in the second period - and then kept going.
''First period, obviously Carter gave us a chance to be even,'' Flyers coach Scott Gordon said. ''That was a huge part of the game.''
''They were the better team in the first period,'' Gordon said. ''It wasn't close. We got better as the game went on. We didn't have a whole lot going and we picked it up afterward.''
It was the first of three meetings this season between the Canadiens and Flyers, who have now beaten Montreal in five straight games dating to the 2016-17 season.
The Canadiens dropped to 3-5-0 in the second game of a back-to-back series after defeating the Columbus Blue Jackets 4-1 on Friday night on the road. It was also the fourth game in six nights for Montreal, while the well-rested Flyers had not played since Wednesday.
But it was the Canadiens who came out flying, outshooting Philly 12-1 in the first period. Philadelphia's only shot was a clearing attempt, though Wayne Simmonds did hit the post.
Montreal was outshooting Philly 16-1 early in the second period, but that's when the Flyers got things started on the scoreboard by scoring twice in a 1:33 span.
Konecny broke the scoreless deadlock at 17:01 for his 12th goal of the season, cashing in a rebound after Antti Niemi made the save on Gostisbehere's initial shot. With an assist on the goal, Sean Couturier extended his points streak to six games.
Van Riemsdyk made it 2-0 at 18:34 when he deflected defenseman Robert Hagg's point shot past Niemi.
The Canadiens were outshooting the Flyers 21-9 when Philadelphia's Jakub Voracek was called for interference on rookie Jesperi Kotkaniemi at 13:33 of the second period. Montreal fired just one shot on net with the man advantage, though, a harmless wrist shot by Jonathan Drouin.
The Canadiens have scored two goals on their last 27 power-play opportunities. They had an 0-for-25 stretch earlier this season.
''The question's been asked of the players and they don't seem to have the answer,'' coach Claude Julien said. ''We keep working at trying to find the answer. It's hard to explain because we're a better 5-on-5 team with those same players than we are 5-on-4. Something there has to get better. The decision-making and the choices of plays have to get better. We're not a threat at all on the power play. Tonight was one power play and it was a dead one.
''It's not easy when your power play generates absolutely nothing. Things seemed to turn from that point on.''
Patrick got his first goal at 7:06 of the third period on a 2-on-1 with Simmonds that put the Flyers up 3-0.
The Canadiens answered back just 30 seconds later when Domi sent a wrist shot off the post.
Patrick restored Philadelphia's three-goal lead with his second goal of the game at 9:32 with a shot in the roof of the net after a nifty dangle to avoid Brendan Gallagher's stick check.
Kulak got one back for the Canadiens with four minutes left, jumping on a loose puck in the slot for his third of the season before Raffl scored the empty-netter with 58 seconds left.
''It was all too little too late,'' said Kulak, who has three goals this season. ''We didn't play our absolute best in the first, but we thought we played well enough to establish a lead - which didn't happen.''
NOTES: Montreal's Paul Byron was serving the second game of his three-game suspension. ... Domi extended his points streak to four games. ... Philly snapped a six-game losing streak on the road.
Flyers: vs. Winnipeg on Jan. 28.
Canadiens: vs. Arizona on Wednesday night.
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