Nashville recorded its third straight win behind Anders Lindback, who started in goal for the first time in almost a month. He picked up his first victory since Oct. 24 by making 28 saves.
O'Reilly, however, slowed down the Carolina comeback bid by scoring 8:44 into the third and Sullivan ended all hopes on an empty-net goal with 2:50 to go.
Cam Ward made 38 saves in the loss. The Hurricanes have dropped six of their last eight.