Maxime Talbot, Harry Zolnierczyk and Wayne Simmonds also scored for the Flyers in the victory tempered by news that captain Chris Pronger will miss the rest of the regular season and playoffs because of severe post-concussion syndrome.
Sergei Bobrovsky stopped 28 shots for Philadelphia, which blew 1-0, 2-1 and 3-2 leads in the second period.
The Flyers have won nine of 10 and are first overall in the Eastern Conference with 43 points, two ahead of Boston and a point behind Minnesota for the overall NHL lead.
Erik Cole scored the Canadiens' third tying goal of the second with 15.5 seconds left in the period.
Louis Leblanc got his first NHL goal and David Desharnais also scored earlier in the middle period for Montreal, which lost in regulation for the first time in seven games (3-1-3).
Carey Price made 21 saves.
In addition to learning they had lost Pronger for the rest of the season, the Flyers also are without star forward Claude Giroux, the NHL scoring leader with 39 points. He missed his second game in a row and is out indefinitely with a concussion after taking an inadvertent knee to the head from Simmonds on Saturday.
Carle got his third point when Meszaros gave Philadelphia its fourth one-goal lead with a slap shot past Price from the point. The Canadiens evened it for the third time in the second moments after Simmonds made it 3-2 at 18:10.
Cole got credit for his team-leading 12th goal on a puck that struck him in front of the net and bounced over Bobrovski and came to rest on its edge just over the goal line inside the right post.
Desharnais erased the Flyers' first one-goal lead 5:02 into the second with a strong individual effort. The Canadiens center held the puck patiently as he carried it out from behind the net, moving his way to the slot to fire a shot past Bobrovksi to tie it at 1.
Zolnierczyk made it 2-1 with his second goal of the season at 5:48.
Leblanc, a Montreal native who was the Canadiens' first-round pick in 2009, drew a huge ovation for his first goal in eight games at 13:24.
Talbot scored his ninth goal 12:07 into the first.
NOTES: Pronger had not played since Nov. 19. ... Canadiens LW Travis Moen missed the game with a lower-body injury sustained Tuesday night in a victory over the New York Islanders.