Tampa Bay also got goals from Eric Brewer, Vincent Lecavalier, Victor Hedman and Steven Stamkos. St. Louis has eight assists and 11 points this season.
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.
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.
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.