Patrick Sharp netted two goals as the Chicago 1, at Nationwide Arena on Tuesday.
Andrew Shaw and Marian Hossa had a goal and an assist and Brent Seabrook also scored for the Blackhawks, who have won four straight. Corey Crawford made 24 saves and Duncan Keith added four assists for the victors.
With the win, the Blackhawks move to within two points of Detroit for fifth place in the Western Conference.
Rick Nash scored the lone goal for the Blue Jackets, who have lost five of their last six games. Steve Mason was torched for all five tallies on 27 shots in defeat.