Malkin scored at 3:40 of the first period, got the go-ahead goal on a power play midway through the third period and had an empty net goal in the final minute for his fifth career hat trick.
Crosby had four assists and Bill Guerin added a goal to secure the Penguins' third win in their last four games. The win moved Pittsburgh ahead of idle New Jersey by two points at the top of the Atlantic Division.
The Islanders, who had a four-game winning streak snuffed out, had goals from Trent Hunter, Andy Sutton, Freddy Meyer and Richard Park.
Crosby put Pittsburgh ahead with the only goal of the first period. Malkin's first goal of the night was one of two power-play goals tallied by the Penguins.
Brent Johnson made 31 saves for the Penguins. Starting goalie Marc-Andre Fleury remained sidelined with a broken finger.
New York's Dwayne Roloson gave up five goals on 28 shots.
Celebrity Families of 2014 [PHOTOS]