Richards set an NHL record by scoring his third career 3-on-5 goal and kicked off a four-goal second period that carried the Flyers to a 5-2 rout of the Rangers on Sunday.
Philadelphia won for the third time in four games and completed a New York, New York weekend sweep after a convincing home win over the Islanders on Saturday.
"We won two very big ones for us," said Martin Biron, who made 35 saves. "We feel pretty good about the situation we're in."
The second-place Flyers are three points ahead of the Rangers in the Atlantic Division and in the race for home-ice advantage in the first round of the playoffs.
New York, which sat atop the division for much of the first half of the season, is close to falling out of a postseason slot. The Rangers, 1-5-2 in their past eight games, started the day seven points ahead of ninth-place Carolina in the Eastern Conference.
"Losing is no fun. Each and every night it kills you and it eats at all of us," said captain Chris Drury, a culprit on Richards' league-leading fifth short-handed goal. "We have to find a way to get wins."
Fans at Madison Square Garden blamed coach Tom Renney and general manager Glen Sather, chanting for their ousters.
"I take full responsibility for where this team is right now," Renney said. "My job is to correct this, get us winning, get us feeling better about ourselves, getting a solution. It's as simple as that.
"It's not any one thing. It's going to have to be a collective effort. We have to come back to what makes us a good team."
With the Flyers ahead 1-0 early in the second period and down two men, Richards took a pass from Braydon Coburn, split Drury and defenseman Michal Rozsival at the blue line, and raced in alone to score on Henrik Lundqvist at 1:18.
Richards partially fanned on the shot but still forced it in off Lundqvist's glove. The Rangers allowed three more goals in the period during a span of 1:49, and Lundqvist was yanked after giving up four on 14 shots.
Steve Valiquette relieved him when Glen Metropolit made it 4-0 at 7:57, and was touched for Mike Knuble's 19th goal 55 seconds later on the first shot he faced.
Claude Giroux, playing his 16th NHL game, scored his third goal -- and second in two days -- to give the Flyers a 1-0 lead 8:12 in.
He then assisted on goals by Matt Carle and Knuble. Carle scored at 7:03. Philadelphia had only 20 shots overall, two during third period garbage time.
Biron allowed a goal to Lauri Korpikoski that made it 5-1 at 12:25 of the second, and another to Nikolai Zherdev with 10:21 left that cut New York's deficit to three.
Lundqvist, who started against the Flyers for just the second time in seven meetings, was long gone by then.
He failed to cover a loose puck in front, and that turned into the Flyers' first goal. Scottie Upshall found Giroux in the slot with a pass, and Giroux scored into an empty net with Lundqvist's back turned to him and the rest of the Rangers standing flat-footed.
The game turned when the Rangers' punchless power play went on a 5-on-3 advantage. New York, in a 1-for-31 power-play drought, got caught for its league-worst 14th short-handed goal. Philadelphia has scored an NHL-high 14 times short-handed.
"I didn't know their history on power plays or short-handed goals," said Richards, who has 20 goals. "Whenever we play, we always try to take advantage of them maybe getting a little bit too relaxed."
Lundqvist got little help from his teammates on the next goal when four guys went to one side while the puck came to Carle, alone to the right. Metropolit made it 4-0 with a shot from the goal line that banked in off Lundqvist's leg.
"Every goal is pretty important. We can't afford too many mistakes," Lundqvist said. "It's a tough one for us. It's a disappointment."