Richards added an empty-net goal with 42 second left, and Darroll Powe scored another empty-netter with 10 seconds left. Glen Metropolit and Braydon Coburn also scored, and Gagne added two assists.
Richards also picked up his league-leading sixth short-handed goal and second in two games. His score on a 5-on-3 disadvantage against the New York Rangers on Sunday was his third such career goal, making him the only player in NHL history to accomplish this feat.
Jaroslav Spacek had two goals, and Derek Roy added a goal and assist for the Sabres, who had won two of their previous three games. Drew Stafford had two assists.
Philadelphia's Martin Biron made 39 saves. Miller stopped 31 shots.
Metropolit put Philadelphia ahead at 12:42 of the first period, redirecting Arron Ashman's shot from the point while standing to the side of the net.
Spacek pulled the Sabres even with his first goal at 3:16 of the second period with a wrist shot that bounced off Biron's glove. After Coburn regained the lead for the Flyers with a one-timer at 8:57 - his first goal in 14 games - and Spacek tied it at 2 with a long slap shot on a power play at 12:11.
Richards scored the Flyers' NHL-leading 15th short-handed goal of the season at 14:03 when his shot from in close hit the post and bounced off Miller's leg into the net. Kimmo Timonen set the play up after Roy turned the puck over deep in the Flyers' zone, skating in and hitting Richards with a pass.
Roy pulled the Sabres even again at 3-3 with 31 seconds left in the period, hammering in a rebound during a scramble in front of the net on a power play.
Notes: Buffalo C Paul Gaustad returned after missing six games with an upper-body injury. ... Philadelphia G Antero Niittymaki was back after being sidelined for two games because of the flu.
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