Stalberg scored two goals and Corey Crawford made 37 saves as Chicago topped Columbus.
Marian Hossa had a goal and an assist, and Patrick Sharp also connected for the Blackhawks, who are 9-1-1 in their last 11 games and lead the NHL with 50 points.
Crawford lost a bid for his first shutout this season when Columbus defenseman James Wisniewski scored at 3:09 of the third period. Crawford was sharp, especially early on, in his second straight start following a string of six consecutive starts by backup Ray Emery.
Steve Mason blocked 18 shots for Columbus, which lost its fifth straight and has yet to win in regulation on the road this season. The Blue Jackets have a league-worst 22 points.