"I thought our team worked hard tonight, and it's nice to see us capitalize," Flyers coach John Stevens said.
With his 31st and 32nd goals, Carter moved one ahead of Washington's Alex Ovechkin for the NHL lead. Richards entered the night with one goal in his previous 12 games.
"The puck kind of followed me," Richards said. "I feel like I was getting the chances before, I just wasn't getting the results."
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, both of which the Tampa Bay players thought the video review process got wrong.
"They have to do better than that," Tampa Bay right wing Mark Recchi said. "We're fighting for our playoff life and calls like that really hurt our hockey club. It's not right. I think they made some mistakes tonight."
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.
"I believe 100 percent it was (a goal)," Stamkos said. "It's a tough thing to swallow. It's a tough loss."
Hartnell and Carter completed the Flyers' three-goal third.
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 Recchi intentionally kicked the puck into the net.
"They made the wrong call," Recchi said. "If you look at it in fast motion, there's no way I can react to that puck. It's a terrible call on their part, and it made a big difference in the game."
Recchi has 533 goals, tying him for 29th place on the NHL career list with Frank Mahovlich.
- Former Secretary of State Condoleezza Rice attended the game. She spent time postgame in the Tampa Bay's coaches room talking with members of the coaching staff and players.
- Lightning backup G Olaf Kolzig was 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.