Duncan Keith, Dave Bolland and Dustin Byfuglien also scored for Chicago, who jumped to a 3-0 lead in the first period. Patrick Lalime made 29 saves.
Fredrik Modin, Dan Fritsche and Rick Nash tallied for the Blue Jackets, who have won only one of nine home games.
Nash, playing his first game since being named Blue Jackets captain, cut Columbus' deficit to 4-3 at 7:15 of the third period with his team-leading 36th goal. Byfuglien pushed Chicago's lead back to two goals three minutes later with his 17th.
Ladd made it 6-3 with a power-play goal with 3:23 remaining.
Barker scored his fifth of the season at 1:00 of the opening period on the Blackhawks' first shot. His drive from a tough angle at the boards near the left circle got over goalie Pascal Leclaire.
Keith made it 2-0 on the power play at 11:21, snapping home a pass from Robert Lang.
Just 1:51 later, Kane curled a backhand shot through traffic that Leclaire couldn't hold. Bolland smacked in the rebound for his fourth of the season, drawing boos from the home crowed.
Columbus coach Ken Hitchcock pulled Leclaire, who allowed three goals on six shots, and replaced him with Fredrik Norrena.
The Blackhawks scored four goals in the first period of their last game against the Blue Jackets, a 7-2 win at Columbus on Feb. 13.
The Blue Jackets scored two goals 27 seconds apart to get within 3-2 in the second period.
David Vyborny weaved through traffic and left a pass for Modin, who missed the previous four games due to a sore groin. He fired a shot through a screen to beat Lalime at 6:27 on the power play. Columbus was 1-for-35 with the man advantage its previous 10 games.
