"It probably wasn't the prettiest game out there, but we'll take the win and hopefully this starts something good," Stamkos said.
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.
"Their goalie played an outstanding game, but simply, our goaltending, me, by myself, have got to do better," said Bryzgalov, who had 11 saves. "That's the bottom line."
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.
"Sometimes, as a goalie, you have to make one key save a game," Garon said of Hartnell's chance.
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.
"He was real solid," Lightning coach Guy Boucher said. "Good goaltenders do that."
Lecavalier scored late in the third.
Hartnell tied it at 1 off the rebound of a Claude 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.
"They're all are not going to be Picasso's," Boucher said. "Real bad first. Real good second."
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.
"What's frustrating is we didn't score goals on our chances," Jagr said. "It looked like nothing went our way. Two weeks ago, everything went our way. That's the business."
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.
Briere had missed the Flyers' previous game due to a right hand injury. He had seven shots on goal. ... 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. ... Philadelphia D Braydon Coburn was minus-4 for the game. ... Tampa Bay RW Martin St. Louis had two assists.