"Go the net, sometimes you get lucky," Craig said. "Being in the right place at the right time. It's good to help the team out."
Craig has 12 goals in 33 games this season.
Vinny Prospal, Fredrik Modin, Vincent Lecavalier and Brad Richards also scored for the Lightning, who won for the third time in nine games. Tampa Bay has won eight straight against Philadelphia, the team it defeated in the 2004 Eastern Conference finals.
"Both teams really look forward to playing against one another," Lightning coach John Tortorella said.
The Lightning are seventh in the East. They have a three-point lead over eighth-place Montreal and are four ahead of ninth-place Atlanta.
"What's disappointing is we had a lot of effort," Flyers coach Ken Hitchcock said. "We made some mistakes. You don't want to waste efforts like we had tonight."
Forsberg put the Flyers ahead 1-0 at 5:56 of the first period. Lightning goalie John Grahame stopped Forsberg's shot, but the rebound hit Tampa Bay defenseman Pavel Kubina and went into the net.
Three straight Philadelphia penalties led to three Tampa Bay goals.
The Lightning tied it 1-1 on the power play when Craig redirected Dan Boyle's shot at 8:17. Prospal scored a 5-on-3 goal from the bottom of the right circle at 12:03 before Craig made it 3-1 just one second after another power play ended with 7:10 left in the first.
Flyers defenseman Derian Hatcher received a 5-minute boarding penalty for a hit on Richards and was ejected 49 seconds into the third.
"He sees me, turns away. You can't stop," Hatcher said. "If he keeps going and takes the hit, it's not even an issue right now."
Kubina was given a roughing penalty in the ensuing scrum.
"My only concern is the butt-end by Kubina," Hitchcock said. "To me, there should be a suspension for that or there should be a review of that at least. He was within an eyelash of taking Hatch's eye out."
Modin scored Tampa Bay's third power-play goal at 5:44 of the third. Carter got Philadelphia within 4-2 on the power play at 6:50.
A mistake by Grahame allowed the Flyers to pull within 4-3 with 5:19 left. He tried to clear the puck up the slot, but the attempt hit Dimitrakos and wound up in the net.
Lecavalier got the goal back with a nifty wraparound with 1:43 left. Lecavalier, who was knocked down after scoring by Philadelphia's Denis Gauthier, received an instigator, fighting and game misconduct penalties for going after the defenseman. Gauthier wasn't given a penalty.
"Vinny gets an instigator penalty. Why? I don't know. Because, he got run over," Tortorella said. "Gauthier knew the puck was in, that play was done. I love the way Vinny responded. I like the way Kubina responded."
The NHL office will review the play.
"He's the one that instigated it by hitting me late after a goal," Lecavalier said. "I definitely don't think I should get suspended."
Richards closed the scoring with an empty-net goal in the final minute.
Flyers C Michal Handzus (shoulder) returned after missing eight games. ... Philadelphia RW Sami Kapanen (sore shoulder) didn't play. ... Tampa Bay was without G Sean Burke, who broke the tip of his right index finger in practice Thursday and is out indefinitely. ... Philadelphia RW Turner Stevenson (hip) sat for the fourth consecutive game.
Copyright by STATS LLC and The Associated Press
Arena: Tampa Bay Times Forum Location: Tampa, Florida
Referees: Eric Furlatt, Kevin Pollock Linesmen: Michel Cormier, Jonny Murray
Attendance: 20,834 (105.4% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Peter Forsberg (17)
Ryan Craig (11)
(Power Play) Assist: Dan Boyle
Vinny Prospal (23)
(Power Play) Assists: Brad Richards, Pavel Kubina
Ryan Craig (12)
Assists: Darryl Sydor, Dan Boyle
No scoring this period
Fredrik Modin (27)
(Power Play) Assists: Darryl Sydor, Vincent Lecavalier
Jeff Carter (16)
(Power Play) Assists: Freddy Meyer, Joni Pitkanen
Niko Dimitrakos (5)
Vincent Lecavalier (31)
Assists: Martin St. Louis, Vinny Prospal