Chosen fifth overall in the 2005 draft, Price won his second straight start, drawing chants of "Carey! Carey!" from the sold-out crowd of 21,293 after Montreal killed a lengthy 5-on-3 early in the third period to protect its slim lead.
"It seemed like it was eight minutes long," Price said. "We worked really hard and the penalty kill, you've got to give them credit. They didn't quit, and they were gunning, too. They're a good power play. They were moving the puck really well."
Price also survived a late panic in the goal crease when the Flyers jammed the net with 1:09 remaining.
Kostitsyn scored on the power play 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.
"He gave me a lesson," Kostitsyn said about Ovechkin's oft-viewed goal on Jan. 16, 2006, when the Capitals' budding superstar swept a puck into the net with his stick past Coyotes goalie Brian Boucher while sliding on his back.
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.
"He's had a couple of highlight goals so far this season and it seems that he can score when you least expect it," Canadiens captain Saku Koivu said.
Montreal won its second in a row following a season-high three-game losing streak.
Philadelphia, which hosts the Canadiens on Sunday night, lost its sixth in a row, matching its longest losing streak of the season.
The Flyers, who have lost five straight to Montreal, including three this season, felt they were denied the tying goal 18:51 into the third.
"The ref was on the right side of the net so he couldn't see it but they didn't even give us the courtesy of going upstairs and looking at the play," Hartnell said. "I don't know what the reasoning was, they didn't explain it that well."
Asked who he thought put the puck on net in the mad scramble, Price said, "Everybody. Ten guys pitchforked me into the net."
Flyers coach John Stevens didn't see the play from the same perspective.
"They made the call on the ice that the goalie was pushed into the net and that didn't happen," Stevens said. "We saw it on the replay. The goalie fell back in the net."
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.