Talbot was part of a sensational penalty kill late in the game that drew a standing ovation and preserved the victory.
The Flyers, clinging to a 2-1 lead, killed off a double-minor by Tye McGinn and a two-minute, five-on-three disadvantage. Talbot, Sean Couturier, Braydon Coburn, Claude Giroux, Matt Read, and Ruslan Fedotenko did most of the PK work, and goalie Ilya Bryzgalov made huge stops on Rick Nash from the right circle and Derek Stepan from the left.
Jakub Voracek, who scored what proved to be the game-winner, called the penalty kill a "game-changer."
"If they score five on three, you say, 'Here we go again,' and then they have another power play," Voracek said. "The boys did a great job."
Second-period goals by Wayne Simmonds and Voracek (power play) propelled the Flyers.
Defenseman Nick Grossmann, who triggered the Flyers' first goal, set the tone with a crunching check on Marian Gaborik early in the first period, igniting the crowd. The Flyers controlled the first period, outshooting the Rangers, 11-5, but goalie Henrik Lundqvist was his usual stellar self.
With 8 minutes, 7 seconds remaining in the second period, Grossmann's point drive deflected off the Rangers' Brad Richards and then off Simmonds' skate and past Lundqvist, giving the Flyers a 1-0 lead.
About four minutes later, after Couturier's shot caromed off the left post, Voracek tapped in a rebound from the crease, increasing the lead to 2-0.
The Flyers played without four regular forwards: Danny Briere (fractured wrist), Scott Hartnell (broken foot), Zac Rinaldo (leg laceration), and Brayden Schenn (one-game suspension).
In addition, defenseman Andrej Meszaros apparently injured his shoulder in the second period and did not return for the third. The Flyers will know more about the severity of the injury on Friday, general manager Paul Holmgren said.
The Rangers (1-3), looking tired in the first two periods after a draining overtime win over Boston on Wednesday, got to within 2-1 on Taylor Pyatt's power-play goal with 18:21 left in the third period.
But the Flyers survived, recording their first win over the Rangers since Feb. 20, 2011. They also ended an overall seven-game losing streak, including last year's four playoff losses to the Devils.
Coburn (four hits), Luke Schenn (three), and Jody Shelley (three) led the Flyers in hits; McGinn won a long, entertaining fight with Kris Newbury; and Grossmann (five blocks) was among those who delivered punishing blows for the Flyers.
Talbot said the Flyers' strategy was to use the body more, figuring the Rangers were worn down from playing the previous night.
"We knew those guys played [Wednesday], so obviously when you can put the puck deep and finish the hits, it's" to your advantage, he said.
"Everyone was willing to dig in tonight," Grossmann said. "From the goalie to the forwards to the D, everyone was willing to do the little things. Everyone paid the price and battled hard, and when you do that, good things happen."
Bryzgalov (18 saves) credited his teammates. "They sacrificed and blocked shots," he said. "I can't say enough words.