The Blue Jackets lost in their home opener after splitting two games with San Jose in Stockholm, Sweden.
Chicago took a 2-0 lead after one period but R.J. Umberger scored the 100th goal of his career while Columbus was shorthanded to bring the Blue Jackets within one just 1:11 into the second.
Sharp then changed the momentum by scoring a shorthanded goal at 9:46 and added a wrist shot 2 minutes later that got by Steve Mason for a 4-1 lead.
Turco picked up his first victory in a Chicago uniform after having lost in his first two appearances. He came to the Blackhawks from Dallas this year after spending nine seasons with the Stars.
Mason allowed five goals on 40 shots.