The Hurricanes saw their five-game winning streak come to an end.
Columbus scored twice late in the first period and then rode the goaltending of Bobrovsky, who will be a member of the Russian Olympic team at the Winter Games in Sochi next month.
Bobrovsky has six career shutouts, having recorded four of them last season in his first campaign with Columbus.
Boone Jenner opened the scoring 15 minutes into the contest and Brandon Dubinsky doubled the lead 1:10 later.
The other Columbus goal came from Cam Atkinson on the power play early in the third.
Anton Khudobin gave up the three goals on 24 shots.