With John Tavares scoring twice in a three-goal first period, New York held a 3-0 advantage at the first intermission.
Carolina got second-period goals from Tuomo Ruutu (power play) and Ray Whitney in less than three minutes, reducing its deficit to 3-2. Tim Gleason's second goal this season created a 3-3 tie at the 11:17 mark in the third, setting up the overtime.
Okposo added an assist, while goalie Martin Biron was credited with making 25 saves on 28 shots for the Islanders, who have split their last four contests.
Manny Legace was beaten four times on 25 shots for the Hurricanes, who equaled a franchise-high streak with their 14th straight contest without a victory (0-11-3).
On the power play, the Islanders went 2-for-4, while Carolina went 1-for-4.