It was the third win this season for the Kings and two of them have come in shootouts.
The game was scoreless deep into the third period before the teams traded goals in a span of 35 seconds.
Dwight King scored shorthanded for the Kings with 6:34 remaining in regulation, but Jeff Skinner quickly tied it on the power play.
After combining for 63 shots during the three periods, the Kings and Hurricanes each managed just one in the five-minute overtime.
Cam Ward took the loss after facing 37 shots.