Randy Jones and Scott Hartnell also scored to help Philadelphia win for the third time in four games.
Vinny Prospal scored for the Lightning, who have lost on consecutive days after a three-game winning streak. The Lightning failed to score on a penalty shot and had two goals disallowed.
Philadelphia took a 2-1 lead when Jones scored on the power play from the low left circle off a pass from Richards at 8:05 of the second. Richards extended the lead to 3-1 with 5:19 remaining in the period.
Tampa Bay's Martin St. Louis shot the puck over the net early in the third on a short-handed penalty shot. Fifty-three seconds after officials disallowed Steven Stamkos' goal because they ruled he knocked the puck into the net with a high stick, Carter scored to make it 4-1 at 7:59.
Hartnell and Carter completed the Flyers' three-goal third. Flyers goalie Antero Niittymaki made several nice saves during a Tampa Bay 5-on-3 power play, and also stopped Jeff Halpern during a breakaway in the second.
Richards put the Flyers ahead 1-0 on a breakaway goal at 7:03 of the first. Prospal tied it at 1 on a power-play goal with 2:05 left in the period.
Tampa Bay also had a goal disallowed after a video review with 37.1 seconds to go in the first. It was decided that Lightning right wing Mark Recchi intentionally kicked the puck into the net. Recchi has 533 goals, tying him for 29th place on the NHL career list with Frank Mahovlich.
Notes: Lightning backup G Olaf Kolzig is scheduled to undergo what is expected to be season-ending surgery on his left forearm Saturday. ... Richards has two goals and four assists during a four-game point streak.
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