Kris Letang scored twice, including a tiebreaking goal in the third period, as Pittsburgh won for the fourth time in five games. Mike Matheson also scored, and Tristan Jarry made 33 saves.
Jordan Eberle and Brock Nelson scored for New York, which has dropped two straight following a season-high eight-game point streak. Semyon Varlamov stopped 15 shots.
Nelson gave the Islanders a 2-1 lead with his fifth goal just 53 seconds into the third period, but the Penguins responded.
Matheson tied it with his first goal for the Penguins at 7:35. He started the rush and eventually finished the play with a wrist shot from the slot.
Letang put Pittsburgh ahead for good at 13:34. His centre-point wrist shot beat Varlamov over the shoulder to the blocker side.
Crosby became the 25th active skater to play in his 1,000th game. He's also the first player in Penguins history to play 1,000 games with the team. Crosby entered his 1,000th game with the eighth-most points in NHL history through 1,000 games.
Pittsburgh handed New York its first regulation loss in nine games on Thursday. It was the first time the Penguins won a game all season without trailing at any point.
But the Islanders took it to Pittsburgh in the first period Saturday, building a 16-4 advantage in shots. Jarry stepped up, and the game was scoreless after one.
Shots were 23-10 in favour of the Islanders when Letang opened the scoring 12:36 into the second. Letang scored 12 seconds into a power play with a blocker-side slap shot from Malkin and Crosby.
Eberle tied it with his seventh goal at 15:28, beating Jarry with a backhand.
MALKIN MISSES TIME
Malkin briefly departed with a little more than five minutes to play in the first period. He returned to the bench four minutes into the second.
Malkin gingerly flexed his right leg and left for the dressing room in the first after slamming awkwardly into the boards when Islanders forward Matthew Barzal spun away from a defensive-zone check attempt.
PENGUINS HONOR CROSBY
The Penguins all took warmups in Crosby's No. 87 jersey to recognize their captain before his 1,000th NHL game. At one point during warmups, his teammates knelt down in unison and replicated Crosby's routine of re-tying his skates.
The Penguins honoured Crosby on the ice with a pregame video. The video featured career highlights and a message from his family and teammates in addition to comments from Mario Lemieux, Steve Yzerman, Steven Stamkos, Patrick Kane, John Tavares and others. Malkin and Letang presented an emotional Crosby with a silver hockey stick, a watch, and a framed mosaic celebrating 1,000 games. Recorded messages of congratulations were also played from others during stoppages in play, including former teammate Phil Kessel and longtime rival Alex Ovechkin.
The Islanders begin a four-game homestand Monday against Buffalo.
Pittsburgh will visit Washington on Tuesday. The Penguins close February with four road games against the Capitals or Islanders.