The win gave Pittsburgh 90 points and boosted it into a tie with Philadelphia for fourth place in the Eastern Conference playoff chase.
Crosby's game-winner broke a 3-3 tie at 9:56 of the third period and gave him a 15-game point streak (eight goals, 17 assists).
Netminder Marc-Andre Fleury made 26 saves on 29 shots for the streaking Penguins, who have won five of their last six contests.
New York's goals were scored by both Ryan Callahan (20) and Brandon Dubinsky (10) in the first and Nik Antropov (27) in the second.
Goalie Henrik Lundqvist was beaten four times on 28 shots for the Rangers, who have dropped three of their last four.