Crosby scored his eighth and ninth goals of the season in the first period and Paul Martin added a tally to gave the Penguins a 3-0 advantage.
First-round draft choice Beau Bennett's first NHL goal with 7:40 left in the middle frame proved to be the game-winner for the Penguins, who racked up their fifth win in six contests.
Marc-Andre Fleury turned aside 27 shots for Pittsburgh.
Stamkos assisted on two goals and Cory Conacher also scored for the Bolts.
Anders Lindback started in goal but allowed three scores on 10 shots and was pulled after the first period.
Mathieu Garon stopped 10-of-11 shots the rest of the way.