Eric Staal scored twice within a minute halfway through the final period, erasing a 2-0 deficit, and Jordan Staal supplied the go-ahead goal less than 2 minutes later as the Hurricanes won a third straight.
Anton Khudobin turned aside 20-of-22 shots to notch the victory.
R.J. Umberger and Derek MacKenzie each scored for the Blue Jackets, who dropped a second consecutive contest on the heels of a club-record eight-game winning streak.
Sergei Bobrovsky made 32 saves for Columbus.
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