New York's club-record losing streak was extended to 14 games. The Islanders last won on Oct. 21. Three of their last six setbacks have come in overtime.
There was no scoring in regulation after R.J. Umberger tied it for Columbus with 13:14 to go in the second period. Voracek's game-winner came after Rob DiPietro had stopped a shot by Kris Russell.
Columbus has won five straight games and improved to 8-1 on the road this season.
The win went to Mathieu Garon, who made 21 saves. DiPietro stopped 30-of-34 shots for the Islanders.