The Penguins recorded a 4-2 win in the best-of-seven series.
The Flyers took a 3-0 lead on Danny Briere's power play goal at 4:06 of the second period, but did not score from that point.
Crosby scored once unassisted and once into an empty net with 28 seconds left in regulation. Ruslan Fedotenko, Mark Eaton and Sergei Gonchar each scored a goal and Evgeni Malkin had two assists.
Marc-Andre Fleury was credited with 22 saves on 25 shots and improved his record to 8-3 against the Flyers over the last two seasons.
Philadelphia's Mike Knuble and Joffrey Lupul both scored in the first period and Briere had an assist.
Martin Biron was beaten four times on 34 shots for the Flyers, who were eliminated in the first round for the second time in their last three post-season appearances.