Filppula's score with 4:19 remaining in the middle period broke a 3-3 tie and was the sixth of seven goals during the period.
Martin St. Louis followed with his 20th goal of the season as the Lightning snapped the Flyers' 10-game winning streak on home ice.
Anders Lindback made 35 saves to earn the triumph.
Jakub Voracek scored twice for the Flyers, who fell at home for the first time since Nov. 7.
Steve Mason started in net but was lifted after two periods. He allowed five goals on 17 shots.
Ray Emery stopped all seven shots he faced in the third.
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