Trailing 4-2 early in the third period, the Flyers began a rally when Claude Giroux scored with 7:12 left in regulation.
Then with Philadelphia shorthanded, Kimmo Timonen unleashed a slap shot from the blue line that bounced off the post and into the net with 9.5 seconds left to tie it up.
In the extra frame, the Flyers again were skating shorthanded when Fedotenko worked a give-and-go with Timonen and whipped a wrist shot past Braden Holtby for the game-winner.
Timonen finished with four assists and Giroux added two more for Philadelphia, which won a second straight and stayed in the Eastern Conference playoff hunt.
Ilya Bryzgalov made 25 saves for the Flyers.
Holtby finished with 29 saves.