Coming into the night, the Blue Jackets were tied for eighth in the West with Minnesota, each with 53 points.
The Wild, coming off a 6-1 loss at home to Edmonton on Friday, were in action at Colorado. The Wild would clinch a playoff spot with a win.
Detroit beat Dallas on Saturday and clinched the No. 7 seed.
The Blue Jackets were on the short end of tiebreakers against both the Wild and Red Wings.
Billed as the biggest regular-season game in franchise history, the Blue Jackets were shut out by Chris Mason before scoring three times in the third period to go 8-1-0 in their final nine — all with the spectre of a playoff spot hanging over them.