Price also survived a late panic in the goal crease when the Flyers jammed the net with 1:09 remaining.
Kostitsyn scored a spectacular power-play goal 3:52 into the second with a second effort play that evokes comparison to a remarkable goal Washington's Alexander Ovechkin scored in Phoenix as a rookie.
The Canadiens won their second in a row following a season-high three-game losing streak.
Philadelphia lost its sixth in a row, matching its longest losing streak of the season.
Kostitsyn stunned Flyers goalie Antero Niittymaki, the entire Bell Centre crowd and all the players on both teams when he scored his 18th goal after sweeping the puck towards the net with his stick while he was flat on the ice and seemingly out of scoring range.
Niittymaki, who made 19 saves overall, stopped Kostitsyn's initial shot as the Canadiens left wing drove across the goalmouth. The Philadelphia goalie ran into trouble when Kostitsyn surprisingly managed to fling the rebound towards the net.
The puck struck Niittymaki's blocker and bounced back towards his pad, which deflected it behind Niittymaki once again and over the goal line.
Ovechkin scored an oft-viewed goal on Jan. 16, 2006, by sweeping a puck into the net with his stick past Coyotes goalie Brian Boucher while sliding on his back.
Notes: Philadelphia also lost six in a row (0-4-2) from Dec. 13-22, beginning with a 4-1 loss to Montreal. ... Flyers Ds Derian Hatcher and Braydon Coburn remained out of the lineup. Hatcher missed his second game in a row because of fluid in his knee. Coburn was sidelined for a fourth straight game as he recovers from a ruptured artery in his buttocks. ... Canadiens D Roman Hamrlik returned to the lineup after missing five games because of a bacterial infection.
