"We're spreading the offense pretty good right now," Stamkos said. "We're not forcing things to certain players. We're making the right play."
The Lightning continued their season-long domination of the third period -- outscoring opponents 13-1 -- with goals by Hedman and Stamkos.
Sean Couturier scored for the Flyers, who were coming off a 7-1 win at Florida on Saturday night. Backup goalie Michael Leighton played in his first NHL game since appearing in two playoff games for the Flyers in 2011.
"They had a step on us," Flyers coach Peter Laviolette said. "They were a more rested team with better jump tonight than we were. We had moments and opportunities where we could have scored, but when you play tight defensive teams, it takes a lot of energy to try and create offense. We didn't generate enough."
Purcell tied it at 1 on the power play at 14:34 of the first.
Brewer made it 2-1 on his third goal this season, a slap shot from above the right circle with 3:50 left in the first. The defenseman had one goal in 82 games last season.
The Lightning converted another power play for a 3-1 lead when Lecavalier scored from the right circle 65 seconds before the first intermission.
St. Louis assisted on all three first-period Tampa Bay goals.
After Hedman had a rebound goal 58 seconds into the third, Stamkos gave Tampa Bay a 5-1 advantage with 7:31 to play.
"When you get a little confidence going, as our offensive players have right now, you try to run with it," Stamkos said. "We know, once we get on a roll, we're a tough team to beat."
Couturier put the Flyers up 1-0 just 59 seconds into the game when his shot from the corner along the goal line eluded goalie Anders Lindback.
"You saw that goal, it's something that shouldn't go in," Tampa Bay coach Guy Boucher said. "Then right after, he just made some crazy saves. At some point he just shuts the door, and that's the mark of great goaltenders."
Lindback finished with 24 saves. Leighton stopped 21 shots.
The Flyers went 0 for 6 on the power play, and could generate just one quality scoring chance during a 4-minute first-period man advantage after taking the 1-0 lead.
"I don't know if it was so much them or if it was us," Philadelphia right wing Wayne Simmonds said. "We didn't get too many shots through. They blocked a lot of shots tonight. I think we could have been better. We didn't get anything going there."
Lecavalier also had a first-period fight with Flyers D Luke Schenn. It was Lecavalier's first fighting major since Feb. 3, 2009. ... Philadelphia is sending C Scott Laughton, taken 20th overall in the 2012 amateur draft, back to Oshawa of the Ontario Hockey League. He was pointless in five games with the Flyers this season. ... Stamkos, who also had an assist, extended his season-opening point streak to five game. He has seven assists and 10 points overall. ... Lightning D Sami Salo had two assists.
Copyright by STATS LLC and The Associated Press
TAMPA, FL - JANUARY 27: Ruslan Fedotenko #26 of the Philadelphia Flyers warms up before the start of an NHL game...