Derick Brassard scored the eventual game- 3, at Nationwide Arena.
Tomas Kubalik, Rick Nash and Ryan Russell all found the back of the net for the Blue Jackets, who halted a two-game losing streak. Curtis Sanford made 32 saves in the victory.
Interim head coach Todd Richards secured his first win behind the bench for Columbus, which won despite playing without center Jeff Carter, who was placed on injured reserve on Friday with a separated shoulder, and forward R.J. Umberger, who is out indefinitely with concussion-like symptoms.
Radim Vrbata, Lauri Korpikoski and Adrian Aucoin all scored for the Coyotes, who have lost three straight. Jason LaBarbara was touched for all four tallies on 32 shots in defeat.