Rookie Paul Stastny, Ossi Vaananen and Marek Svatos scored for Colorado. Joe Sakic had an assist to tie Stan Mikita for 14th on the career list with 926.
The Blue Jackets, who have been shutout in five of their 17 games, have lost four straight and 11 of 14.
The game was the second for Columbus interim coach Gary Agnew, who replaced Gerard Gallant after Gallant was fired Monday because of the team's slow start. Agnew lost his debut Wednesday against Nashville.