Both of Cooke's goals were unassisted -- including a shorthanded tally -- and he also set up Dustin Jeffrey's go-ahead marker early in the third period as Pittsburgh logged its third win in four contests.
Marc-Andre Fleury improved to 30-14-3 on the season, making 27 saves.
Philadelphia dropped its sixth game in eight tries despite Jaromir Jagr's two goals in an 18-second span.
Ilya Bryzgalov started in net for the Flyers but exited after yielding three Pittsburgh goals on 13 shots.
Sergei Bobrovsky relieved and posted 14 saves.
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