Leighton notched his second straight shutout and raised his record to 4-0 in post-season starts for the Flyers since taking over for the injured Brian Boucher during the conference semifinals against Boston.
Leighton was especially tough in the first period, when the Canadiens carried the play after spotting Philadelphia a 1-0 lead on Danny Briere's ninth post-season goal 4:16 into the game.
Simon Gagne and Ville Leino added power-play goals for the Flyers, who won their sixth straight game after falling behind 0-3 in the Boston series. They need only two more wins to make their first Stanley Cup finals appearance in 13 years.
Jaroslav Halak stopped 20 shots for the Canadiens, losers of six straight playoff games to Philadelphia.
Game 3 is set for Thursday in Montreal.