Crosby, who entered the game tied with Boston's Brad Marchand in the goals race, moved into a tie with Edmonton's Connor McDavid for the league scoring lead, 80 points apiece.
Crosby has six goals in his past four games. For his 10th career hat trick, Crosby's wingers, Jake Guentzel and Conor Sheary, assisted on each of his goals.
Fleury picked up his 44th career shutout, his second against Florida and his first of the season. He improved to 18-8-6, including 12-3-3 in his past 18 decisions.
The Penguins (45-17-9) are 7-1-1 in their past nine games. They have at least a point in nine straight meetings with Florida, 7-0-2.
The loss further diminished the playoff hopes of the Panthers (31-29-11), who are six points out of a wild-card spot with 11 games remaining.
A clever play by Phil Kessel and a heads-up reaction by Patric Hornqvist led to the only goal of the first period. Kessel lobbed the puck over the net from behind. Hornqvist swung baseball-style and batted it out of the air past goaltender James Reimer for a 1-0 Pittsburgh lead at 16:14.
Crosby then went to work. He scored his 38th from the right dot at 14:15 of the second for a 2-0 Penguins lead.
He added No. 39 at 16:07 of the second on a spinning backhander from the slot for a 3-0 lead.
No. 40 and the hat trick came at 5:00 of the third when Crosby one-timed a feed from Guentzel to make it 4-0. It's the second time in his career that Crosby, 29, has reached 40 goals.
NOTES: Pittsburgh C Evgeni Malkin (right shoulder) missed his second game in a row. He is day to day. The team's number of injured players remains at seven. ... Florida RW Jaromir Jagr became the fourth NHL player to reach 1,700 games. The Penguins ran a video tribute to the former Pittsburgh player during the first TV timeout. ... Linesman David Brisebois left with 1:35 left in the first period after he got leveled on hit in the back by Pittsburgh's Patric Hornqvist as Hornqvist rushed forward on a faceoff. Brisebois returned for the start of the second. ... The Penguins' healthy scratch was D Cameron Gaunce. ... The Panthers' healthy scratches were C Michael Sgarbossa and D MacKenzie Weegar.