Fleury posted his second shutout of the season and 13th of his career, while Chris Minard and Tyler Kennedy added goal for Pittsburgh.
The Penguins have won three of their last four games and moved back into playoff position in the Eastern Conference.
Crosby was back in the lineup after sitting out Friday's game with an apparent knee injury. He missed a penalty shot early in the second period and saw his five-game scoring streak end. Crosby was hurt during Wednesday's loss to Washington.
The Rangers' three-game winning streak ended as they were shut out for the third time this season. New York hasn't won in regulation at Mellon Arena in the past 12 games, including playoffs.
Fleury has allowed only one goal in his past two games. The Penguins traded for Mahieu Garon on Saturday to perhaps push Fleury, the No. 1 overall pick in the 2003 draft who has been spectacular times but inconsistent at others.
Fleury had a 2.94 goals-against average and .905 save percentage and had given up at least four goals during seven of his past 17 starts, causing Penguins coach Michel Therrien to publicly question his team's goaltending.
Some of Fleury's better saves Sunday included stops of Markus Naslund late in the first period and denying Chris Drury from right in front during a 4-on-3 situation late in the second.
Minard scored on a one-timer from the slot off a pass from Sykora 7:35 into the game.
Kennedy made it 2-0 eight minutes later when he skated in from the right point and fired a wrist shot from the inner edge of the top of the faceoff circle, beating Rangers goalie Henrik Lundqvist for his eighth of the season — but first at home.
Sykora made it 3-0 with his 17th goal while on the power play 7:32 into the second. Jordan Staal won a faceoff in his own end back to Ryan Whitney, who carried the puck out of his zone and found Sykora, who was behind the defense and beat Lundqvist with a wrist shot.