Tampa Bay (11-9-3) has won three straight and four of five including a 5-2 victory over the Flyers in their only other meeting this season on Nov. 14.
"I don't want to say that we have their number," Richards said. "They're a good team and they can beat anybody any night."
Tampa Bay, which eliminated Philadelphia in the 2004 Eastern Conference finals on the way to the championship, has won six straight regular-season games from the Flyers.
"The Flyers are a team that we usually play hard against," said Tim Taylor, who had a goal and an assist. "You know that if you don't play well, you're going to get embarrassed by them. They usually bring out the best in us."
Tampa Bay coach John Tortorella says the Lightning are finally "finding ways to get it done" against the Flyers.
"We were a bit of a punching bag for a while for them," Tortorella explained. "The last time we played them, it was a game that we really felt we wanted to try to get our identity back. I thought tonight the most important part of our game was our puck control down low.
"They have some quality people up front as their offense shows, so we wanted to try to spend as much time in their end zone as we could."
R.J. Umberger and Jon Sim scored for the Flyers, who have dropped four of five.
"We beat ourselves again," Sim said. "We've got a great team, but we have to put our work boots and our work hats on and do the digging in. We're not doing that for 60 minutes."
Richards gave the Lightning a 2-1 lead at 15:35 of the second period when he one-timed a rebound of a shot by Fredrik Modin from between the circles.
Boyle took Rob DiMaio's cross-ice pass and scored from the right circle at 17:01 to make it a two-goal advantage for Tampa Bay.
Taylor scored during a scramble at the goal mouth at 6:25 of the third period to extend the Lightning lead to 4-1. Sim got the Flyers closer at 13:15 on a give-and-go with Michael Handzus on a power play.
Cibak put the Lightning ahead 1-0 at 4:14 of the first period, flipping the puck in from the slot after taking a centering pass from Taylor. It was Taylor's first assist of the season.
Umberger tied it at 12:16 of the period when he scored his first NHL goal on a wraparound. The puck kicked off the stick and skate of Lightning goaltender Sean Burke, who stopped 30 shots.
"Their team was really quick on every loose puck and that's where they beat us," said Philadelphia defenseman Eric Desjardins, who returned after missing eight games with a concussion. "Every time there was a battle we came up short."
- Tampa Bay C Vaclav Prospal's franchise-best 13 game scoring streak (8-13-21) ended.
- Philadelphia C Peter Forsberg played in his 600th NHL game.
- Philadelphia LW Brian Savage (sprained knee) and D Dennis Seidenberg (broken right wrist) were scratched.
- Lightning LW Chris Dingman was a healthy scratch.
- Both of Cibak's goals this season were scored against Philadelphia.