Pittsburgh (45-17-9, 99 points), which is 7-1-1 in its past nine games, is one point behind the Washington Capitals and Columbus Blue Jackets for first place in the Metropolitan Division.
The hat trick was Crosby's first since Feb. 2, 2016, when he had four points (three goals, one assist) in a 6-5 win against the Ottawa Senators. He has five goals in his past two games, each without Malkin, and six goals in his past four games.
The Penguins have won two straight without Malkin, who is day to day with an upper-body injury.
"I think everybody wants to collectively make sure that we make up for the guys that are out," Crosby said.
Fleury earned his first shutout since Feb. 29, 2016, when he made 30 saves in a 6-0 win against the Arizona Coyotes. He is 11-3-3 in his past 19 decisions since losing five straight (0-3-2) from Nov. 3-25.
"It's been awhile," Fleury said. "I was happy to make it until the end. There were a few series in there that were fun, but I thought our guys did great. … We didn't give them too many chances 5-on-5."
Florida (31-29-11, 73 points) is six points behind the Toronto Maple Leafs for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.