Jaroslav Balastik, Manny Malhotra and Duvie Westcott also scored as Columbus went 3-for-8 on the power play and spoiled Chicago's home opener before a crowd of 17,133.
Pascal Leclaire stopped 17 shots.
Adrian Aucoin, Jeff Hamilton, Patrick Sharp and Martin Havlat scored for the Blackhawks.
Chicago's Nikolai Khabibulin had 19 saves, but has allowed 11 goals in his first two starts. The Blackhawks won 8-6 at Nashville on Thursday night.
Chicago was outshot 13-2 in the first period, but scored on both attempts to take a 2-0 lead.
Aucoin opened the scoring at 5:31 when Radim Vrbata's centring pass deflected in off Aucoin's skate. The goal withstood a video review. Hamilton then had a power-play goal through a screen from the right point at 7:16.
The Blue Jackets responded with two power-play goals late in the first to tie the score 2-all. Nash cut it to 2-1 with 5:01 remaining, knocking in a rebound from the left side of the net. Balastik tied it with 2:37 to go, converting a rebound of Anders Eriksson's shot from the point.
Malhotra made it 3-2 with 9:11 left in the second, scoring Columbus's third straight power-play goal.
Following Duncan Keith's turnover, Nash took a pass from David Vyborny, broke in alone and beat Khabibulin 55 seconds later. Westcott made it 5-2 with 6:27 left in the period, banking in a shot off Khabibulin's pads from the side of the net.
Sharp's power-play goal with 4:19 left in the third cut Chicago's deficit it to 5-3. Havlat fired in a loose puck from the side of the net with 3:56 remaining to make it 5-4.
Notes: Havlat has three goals and three assists in his first two games with the Blackhawks. ... Out with long-term injuries for Chicago are G Patrick Lalime (back surgery, three months), F Tuomo Ruutu (sprained knee, four weeks) and D Cam Barker (ankle surgery, four to six weeks) ... D Bryan Berard (back) and F Sergei Fedorov (shoulder, four to six weeks) are long-term injuries for Columbus. ... Blue Jackets D Rotislav Klesla served the second game of a two-game suspension for clipping Ruutu in an exhibition game at Columbus on Sept. 22. ... Hamilton's goal was his first with the Blackhawks and third of his career. Formerly in the New York Islanders' organization, Hamilton was signed by Chicago as a free agent on Sept. 29 after a strong training camp.