"Alain told our line that it was our job to get it done offensively," Savage said. "It was up to us to put the goals on the board."
Savage's linemate Martin Rucinsky got the first goal of the game, and Corson and Turner Stevenson also scored for the Canadiens (6-5-2), who have won three straight.
Alexandre Daigle scored the lone goal for the Flyers (5-5-4), who are winless in their last six (0-4-2).
"In the first period we got beat to all the loose pucks," Flyers forward John LeClair said. "We didn't come out with the desire we needed to win, so we fell behind early. We're definitely looking for ways to win, but the way we came out, we're not going to do it like that."
Rucinsky, who missed the first six games of the season because of a contract dispute, scored his second goal of the year after taking a pass from Savage and beating Philadlphia goaltender John Vanbiesbrouck with a high wrist shot at 15:37 of the first period.
Just fifteen seconds later, Rucinsky set up Savage in front of the net to make it 2-0. The Canadiens outshot Philadelphia 9-4 in the opening period.
Daigle scored Philadelphia's only goal midway through the second period. His shot from the faceoff circle trickled through goaltender Jose Theodore's legs.
Stevenson restored Montreal's two-goal lead before the end of the period, beating Vanbiesbrouck from the side of the net.
After that, the defense did the rest.
"You can't give enough credit to Recchi, Corson and Damphousse," Savage said. "They shut down (Eric) Lindros and LeClair and played good defensive hockey."
Lindros failed to register a shot in the first period and wasn't a physical presence. He was shadowed by Damphousse the entire night.
"What I tried to do was to position myself properly," Damphousse said. "LeClair is a finisher, but Lindros is the one who sets him up. If he gets the puck in the neutral zone, he can make that pass to LeClair. I tried to make them get rid of the puck as soon as possible and not give them time on the puck."
LeClair was also foiled on a breakaway by Theodore in the second period.
"I think if I score on that, it eventually ends up as a 2-2 game," LeClair said. "It might have been a different outcome."
Theodore shone in the second and third periods, when the Flyers outshot Montreal 27-10.
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