The score was tied 2-2 after two periods, but Stalberg put the Hawks ahead to stay 4:26 into the final frame.
Nick Leddy poked a puck past a Columbus defenseman at the right point, and Stalberg skated in alone on net, sending a wrist shot past rookie goalie Allen York for the lead.
He scored again only 2 minutes later for Chicago, which improved to 6-0-2 in its last eight games.
Vinny Prospal and Derek MacKenzie lit the lamp and York finished with 33 saves for the Blue Jackets.
Notable deaths of 2014 [PHOTOS]