Jagr scored with 43.6 seconds left in the extra frame, allowing the Flyers to avoid a season's sweep at the hands of Winnipeg.
Ilya Bryzgalov collected the win with 22 saves.
The Jets' three-game winning streak was snapped despite a pair of Andrew Ladd goals.
Pavelec logged the second 50-save game in his career. He also pulled off the feat in a 3-1 win over Ottawa in October 2009.