Richards, who leads the NHL with five short-handed goals this season, became the first NHL player to score three 3-on-5 goals in a career.
That took the air out of the Rangers, who allowed three more goals in the period during a span of 1:49. Lundqvist was yanked after giving up four goals on 14 shots.
Steve Valiquette relieved him when Glen Metropolit made it 4-0 at 7:57, but he wasn't spared. He was touched for Mike Knuble's 19th goal 55 seconds later on the first shot he faced.
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 into the first. He then earned assists on goals by Matt Carle and Knuble. Carle scored at 7:03. Philadelphia finished with five goals on 20 shots.
New York fell to 1-5-2 in its last eight games and dropped three points behind second-place Philadelphia in the Atlantic Division. The teams, which hadn't faced each other since opening week, will meet four more times.
Philadelphia started its scoring binge Saturday in a 5-1 home win over the New York Islanders. The Flyers scored a pair of goals 44 seconds apart in the first period and then added three within 1:07 of the third to break that one open.
Martin Biron was the beneficiary of both outbursts. He finished with 35 saves, allowing 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 goals.
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 while short-handed.
Richards broke in alone and slammed a shot in off Lundqvist's glove for his 20th goal.
Lundqvist also 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 of the goalie for a snap shot. Metropolit made it 4-0 with a shot from the goal line that banked in off Lundqvist's leg.
That brought Valiquette off the bench amid various chants from the frustrated crowd that calling for the firings of Rangers coach Tom Renney and general manager Glen Sather.
Notes: Scott Munroe, who has yet to make his NHL debut, served as Biron's backup for the second straight day. Antero Niittymaki was scratched again because of the flu. ... The Rangers play at St. Louis on Monday.
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