The Avalanche had a five-game home unbeaten streak snapped.
The game was scoreless until Milan Hejduk netted his 16th goal 3:31 into the third to extend his points streak to a career-high 10 games and put Colorado on the road to its fifth win in seven contests.
But Jeremy Roenick scored late in the third to send the game to overtime and Desjardins beat goaltender David Aebischer at 1:38 to give Philadelphia just its second win in the last 11 road contests against the Colorado franchise.
Roman Cechmanek turned aside 34 shots for the Flyers, who improved to 5-1-2-0 in their last eight overall.
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