Guillaume Latendresse and Mikko Koivu scored for Minnesota.
Steve Mason had 32 saves for Columbus. Minnesota's Josh Harding stopped 22 shots.
Latendresse opened the scoring at 11:17 of the first period before the Blue Jackets countered with three goals in the second period behind Tyutin, Nash, and Carter on the power play.
Koivu pulled the Wild within one with a man-advantage goal at 8:10 of the third period, and Atkinson made it 4-2 six minutes later.