On the play, Crosby stripped New York's Thomas Vanek of the puck at the blue line and turned toward the net. The NHL's leading scorer split two defenders and put the puck past Anders Nilsson for the game-winner.
Crosby also supplied a score-tying, power-play goal in the third period for the Pens, who battled back from an early two-goal deficit for a fourth straight win.
Kyle Okposo netted a pair of goals for the Islanders.
Nilsson finished with 31 saves.