The contest was tied, 3-3, after regulation because Pittsburgh's Petr Sykora scored his ninth goal this season at 14:28 of the third to create the deadlock.
Pittsburgh squandered an early 2-0 lead. New York's Michal Rozsival scored twice in the second.
Goaltender Marc-Andre Fleury was beaten four times on 26 shots for the Penguins, who have lost five of their last six.
Crosby has a point in every game this season except the opener, and his scoring total rose to 30 points (11 goals and 19 assists).
In man-advantage situations, New York was 1-for-6, while the Penguins went 0-for-1.