Khudobin was 50 seconds from his third career shutout when Boone Jenner deflected in a Ryan Johansen shot for Columbus' only goal.
Nathan Gerbe, Andrei Loktionov and Patrick Dwyer scored for the Hurricanes, who snapped a two-game overall losing streak and won for just the second time in their last nine road games (2-7-0).
The Hurricanes won the last meeting between the teams 3-2 at home on Jan. 27 to snap a seven-game losing streak in the series. They had lost four in a row in Columbus since their last victory in the city on March 8, 2004.
The Blue Jackets fell to 6-1-1 in their last eight. Sergei Bobrovsky gave up three goals on 20 shots.
Gerbe scored the first one just 3:41 into the game. With Columbus defenseman James Wisniewski in front of him, Gerbe held for a shot from the right circle and beat Bobrovsky with a wrister to the far side.
Loktionov scored on a power play 2:23 into the second period, tapping in a rebound after Bobrovsky stopped Jay Harrison's shot.
Dwyer later beat Bobrovsky's glove with a rifled slap shot from the right side to make it 3-0 with 2:40 left in the second period.