The score was tied 2-2 midway through the third period when Keith Aulie launched a shot from the left point, and Purcell, skating through the crease, deflected the puck past Ilya Bryzgalov for the decisive score.
Stamkos' career milestone came on an empty-netter -- his league-leading 21st goal of the season -- and sealed the Lightning's third win in four games.
Ondrej Palat and Tom Pyatt also scored while Anders Lindback made 28 saves for the Bolts.
Max Talbot and Claude Giroux each scored for the Flyers, who fell to 2-5-0 in their last seven games.
Bryzgalov ended with 23 stops.