Richards batted in a rolling puck off the rebound of a Brandon Dubinsky shot 5 1/2 minutes into the final frame to break a 2-2 tie and Lundqvist stopped a penalty shot in the final minute to preserve the 2012 Winter Classic win for the Rangers at Philadelphia's Citizens Bank Park.
Daniel Briere was awarded a penalty shot with 19.6 seconds remaining when the officials ruled Rangers defenseman Ryan McDonagh closed his hand around the puck in the crease.
Briere tried to shoot it between Lundqvist's pads, but the New York goalie made the save -- one of 34 in the contest as the Eastern Conference-leading Rangers opened a four-point lead over the fourth-place Flyers.
Michael Rupp scored consecutive goals late in the second period and early in the third to erase a 2-0 Philadelphia lead.
Brayden Schenn scored his first career goal and Claude Giroux added a tally, while Sergei Bobrovsky finished with 30 saves for the Flyers.