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.
Notable deaths of 2014 [PHOTOS]