Fleury took a shutout deep into the third period, by which time the Penguins had wrapped up a win in their bid for a second straight Eastern Conference title.
Pittsburgh fell to Detroit in last year's Stanley Cup Finals and then got off to a poor start this season before putting together an excellent second half to the campaign and earning a No. 4 seed.
Crosby, who scored 33 goals with 70 assists in the regular season, produced a power-play score 4:41 into the contest.
Tyler Kennedy added a goal 1:39 into the second period and Pittsburgh ensured its victory with goals from Evgeni Malkin and Mark Eaton during the opening half of the third stanza.
Philadelphia could not get to Fleury until Simon Gagne scored on the power play with 4:35 remaining.
Martin Biron allowed all four goals on 33 shots. Philadelphia will try to even the series Friday.