The Flyers lost despite outshooting the hosts, 32-16.
Unlike when the Flyers were here in November, Tampa rarely used its 1-3-1 neutral-zone trap.
Tampa Bay, which started the night 13th in the 15-team Eastern Conference, took a 2-1 lead as Bryzgalov failed to control a rebound and was beaten by Stamkos with 12 minutes, 35 seconds left in the second period. It was Stamkos' 21st goal, and it gave the Lightning two goals on just seven shots against the struggling Bryzgalov.
About seven minutes later, former Flyer Steve Downie made it 3-1 by scoring off another rebound.
With the Flyers down by two goals, winger Wayne Simmonds tried to spark his team when he pounded Eric Brewer with 7:28 remaining in the second period. The Tampa Bay defenseman was dazed, bleeding, and had to be helped off the ice.
Tampa Bay increased the lead to 4-1 on Stamkos' power-play goal with 1:15 to go in the second period. It was scored while Max Talbot was serving a double minor (boarding, unsportsmanlike conduct).
Stamkos' second goal of the night, tying him for the NHL lead pending Tuesday's results, gave the Lightning four goals on 10 shots against Bryzgalov, who took just an .895 save percentage into the game.
The Flyers will be in Pittsburgh Thursday before returning to face the New York Rangers in the Winter Classic on Monday.
After Tuesday's morning skate, Flyers coach Peter Laviolette said he didn't think the Flyers would look past the Lightning or Penguins and ahead to the hyped-up Classic.
"The teams that find success and find themselves pushing at the top of the conference are the ones that stay focused on the job at hand, day to day," he said. "I have not mentioned" the danger of looking past teams. "They seemed sharp out there this morning."
They carried it into the opening period, dominating every aspect except on the scoreboard.
The Flyers outshot the Lightning, 17-4, in the first 20 minutes but needed a late goal by Scott Hartnell to take a 1-1 tie into the first intermission. Hartnell scored on a rebound after Claude Giroux deliberately fired the puck off the end boards and then shot it on net. Garon, who was brilliant in the first period, made the save, but Hartnell buried the rebound.
It was Hartnell's 17th goal, tying him with Giroux for the team lead.
"Good things happen when you go to the net," said Hartnell, who has 11 goals in his last 17 games.
The holiday break, Hartnell said before the game, was good for him.
"It was nice to spend a couple days at home and stay in bed and just relax," said Hartnell, who was stopped on an early breakaway. "Any days off help you down the stretch."
Earlier in the first period, Tampa Bay scored on just its second shot, as defenseman Bruno Gervais beat Bryzgalov with a long drive. Bryzgalov may have been screened, and the shot appeared to deflect off the stick of teammate Brayden Schenn.
While the Flyers excelled in even-strength situations early in the game, they struggled on the power play, failing to get any shots on their first three man advantages in the first two periods.
Tampa was playing shorthanded because one of their top defensemen, Victor Hedman, was injured in the first period and did not return.
Contact staff writer Sam Carchidi at email@example.com or @BroadStBull on Twitter.