The Lightning went ahead 2-1 on Stamkos' rebound backhand at 7:25 of the second.
After Steve Downie scored at 11:41, Stamkos got his 22nd goal of the season to make it 4-1 with 1:15 remaining in the second.
Bruno Gervais and Vincent Lecavalier also had goals for the Lightning, who had lost four of six. Defenseman Victor Hedman left in the first period with an upper-body injury.
Scott Hartnell scored for Philadelphia, which is 1-3-1 over the past five games. Flyers goalie Ilya Bryzgalov gave up Tampa Bay's first three goals on just eight shots.
Gervais put Tampa Bay ahead 1-0 at 9:34 of the first. The goal came after Garon stopped in-close shots by Matt Read and Danny Briere, and made a save on Hartnell during a breakaway in the opening seven minutes.
Garon has supplanted Dwayne Roloson, who led the Lightning to the Eastern Conference finals last season, as Tampa Bay's primary goalie. Garon has played in 14 of the Lightning's past 16 games.
Lecavalier scored late in the third.
Hartnell tied it at 1 off the rebound of a Giroux shot with 1:46 left in the first. Philadelphia outshot the Lightning 17-4 in the first period.
Philadelphia went almost 10 minutes without a shot in the second and finished with three in the period.
Claude Giroux has 27 assists and 44 points this season. Jaromir Jagr also assisted on Hartnell's goal, giving him 972 assists and 1,629 points in 1,304 career games.
Unlike the Flyers' 2-1 overtime loss at Tampa Bay on Nov. 9, Philadelphia only used a stall tactic in its own end several times in response to the Lightning's 1-3-1 defensive zone.
In last month's game against the Lightning, the Flyers utilized the strategy seven times alone in the first period and ended with just 15 shots in the game.
Notes: Briere had missed the Flyers' previous game due to a right hand injury. ... Tampa Bay RW Adam Hall stopped a personal 26-game point drought with an assist on Gervais' goal. ... Flyers C Brayden Schenn was in the lineup after sitting out nine games because of a concussion. ... Lightning D Matt Gilroy could return soon from an undisclosed lower-body injury.