Troy Brouwer, Cam Barker, Rene Bourque and Jonathan Toews scored for Chicago.
Down 2-0 after 20 minutes, the Blackhawks scored three times - twice with a two-man advantage - in the second period to take the lead.
Columbus' Rick Nash scored from close range on a two-man advantage with under three minutes left in the game to make things interesting.
Jason Chimera and Kris Russell also scored for Columbus, which has lost its two pre-season contests, both at home. Derick Brassard and Duvie Westcott had two assists apiece for the Blue Jackets.
Chicago's Patrick Kane, selected first overall at this year's entry draft in Columbus, did not play. He is expected to make his debut Wednesday at home against the Blue Jackets.