Brian Boucher made 34 saves, but wasn't severely challenged until the Rangers staged another third-period comeback try. He fell short of his 18th NHL shutout when Wojtek Wolski scored with 10:29 remaining. Derek Stepan brought New York within a goal 2:24 later.
The only other downside for the Flyers, who finished a 3-1 road trip, was the end of Danny Briere's five-game goal streak.
Jeff Carter and Leino scored seconds after the expiration of two power plays in the first period, and Richards stretched Philadelphia's lead to 3-0 in the second with his 23rd career short-handed goal. Flyers defenseman Matt Carle assisted on both first-period scores and had a spirited fight in the second in which he took several punches to the head from Sean Avery.
Philadelphia won for the sixth time in seven games and moved one point behind Vancouver for first place overall in the league standings. The Flyers are tied for the NHL lead with 16 road wins (16-5-3), one more than New York.
The Rangers wrapped up a rough week in which they lost three times, including twice to Montreal - one at home and one on the road with a 1-0 win against Vancouver in between. They were done in for the second straight night by a poor first period. Montreal scored all its goals within a 2:46 span of the opening frame en route to a 3-2 win on Saturday.
No. 1 goalie Henrik Lundqvist was the tough-luck loser in that one and earned a rest on Sunday. Martin Biron couldn't hold off the Flyers and finished with 24 saves. The Rangers pulled Biron for an extra skater after an icing with 1:41 left, but couldn't notch the tying goal.
The Flyers are 3-0 against the Rangers this season, earning an earlier pair of 4-1 wins.
Many Philadelphia fans made their way north during the holiday weekend to see their team, which has played only one home game since Dec. 20. The Flyers are 7-3 in that span - including 6-3 in the road games.
Boucher made several pad saves that sent thuds through an arena that was otherwise quiet because of the passive crowd. That made it easy to hear the vocal Flyers supporters sound "Boooosh" chants for the goalie.
Other than Avery's fight with Carle during a big melee in the second period, the biggest cheers were reserved for updates on the New York Jets' NFL playoff victory at New England - until the Rangers rallied.
Just 12 seconds after Brandon Dubinsky served a hooking penalty, Carter deflected in Carle's left-point shot as he was left unchecked in the slot at 6:14. Leino doubled the Flyers' lead with 5:06 remaining in the first, taking a crisp feed in front from behind the net from Andrej Meszaros and putting in his 11th goal.
Richards then finished a fine passing play with Claude Giroux and notched his third short-handed goal of the season to make it 3-0 at 4:25 of the second.
Wolski got things started when he beat Boucher from a tough-angle along the goal line. Stepan made it 3-2 with 8:23 remaining off a perfect feed in front from Mats Zuccarello for a one-timer that produced his 13th goal.
Notes: The Flyers have won four straight against the Rangers, their longest streak in the series since a five-game run during the 2003-04 season. ... Boucher has earned wins in four in five outings. ... The Flyers and Toronto Maple Leafs are the only NHL teams without a shutout win this season. ... The Rangers are 10-2 in the second half of back-to-back games. ... Wolski has two goals in four games with New York - including the winner against Vancouver - since being acquired from Phoenix.