Mike Johnson, Alex Kovalev, and Michael Ryder also scored for the Canadiens, who won their second straight. Tomas Plekanec and Andrei Markov each had two assists for Montreal.
Jeff Carter and Joni Pitkanen scored goals for the Flyers, who have won only three home games, the fewest in the NHL.
Higgins broke a 2-2 tie at 8:17 of the second period when he redirected a shot from the point by Francis Bouillon high into the net. Ryder added a power-play goal with a wrist shot from the left circle at 7:10 of the third period.
The teams combined for three goals within a span of 55 seconds early in the first period.
Johnson put the Canadiens ahead at 5:00 when he put in his own rebound.
Carter tied it at 5:25 with a deflection of a shot by Alexei Zhitnik.
Kovalev regained the lead for Montreal 20 seconds later when he scored from the right side after taking a cross-ice pass from Markov.
Pitkanen pulled the Flyers even 1:56 later with his first goal of the season, a one-timer that slipped between the pads of Montreal goaltender David Aebischer, on a power play.
Aebischer had 34 saves. His most spectacular play came late in the second period when he slid midway between the circles to knock a loose puck away from Simon Gagne on a breakaway attempt. He also blanked the Flyers on four power plays in the third period, including 1:43 of a two-man advantage.
Philadelphia goaltender Antero Niittymaki, who has dropped his last 12 decisions (0-11-1), stopped 22 shots.
Eric Desjardins, who played for 11 seasons as a Flyers defenceman, was honoured in pre-game ceremonies with gifts from the Flyers and Canadiens, his first NHL club. Desjardins retired last summer after suffering a concussion, shoulder, and hip injuries.
Notes: Montreal's Plekanec and Sheldon Souray hit the left post and crossbar, respectively, within a 17-second span midway through the first period. ...The Canadiens began a three game road trip in five nights. ... Montreal LW Garth Murray returned after missing three games with a bruised hand. ... Philadelphia C Peter Forsberg returned after missing four games with a strained groin. ... Philadelphia LW Kyle Calder appeared in his 400th NHL game. ... RW Sami Kapanen played in his 200th game as a Flyer.