The game marked the return of former Tampa Bay stalwart Vincent Lecavalier, who scored a power-play goal in the third period that sparked a brief surge by the Flyers.
Lecavalier played 14 years with the Lightning before moving to the Flyers and was honored by a lengthy video tribute prior to the game.
Victor Hedman scored twice for the Lightning, including a power-play goal five minutes deep in the third period that produced a 3-0 lead.
Philadelphia then came up with goals by Lecavalier and Mark Streit in the span of 40 seconds with Streit's goal coming just 1:13 from the end of regulation.
Lindback then held on to get the win with 19 saves and Tyler Johnson sealed the victory with an empty-net goal.
Ray Emery stopped 31 shots for the Flyers.