Pittsburgh won for the ninth time in 10 games, overcoming a two-goal deficit in the third period. The Penguins avoided what would have been their first overtime loss this season.
Ruslan Fedotenko brought the Penguins within one by scoring on a wrist shot with 2:56 to play in regulation and Crosby then assisted on Alex Goligoski's game-tying goal 39 seconds later.
Crosby's shootout goal came in the second round, leaving Kristian Huselius needing to score for Columbus to keep the game going.
Brent Johnson, turned aside the attempt by Huselius, sending the Blue Jackets to their third straight loss.
Johnson made 29 saves for the win. Steve Mason also made 29 saves for Columbus.