The Islanders extended their club-record losing streak to 14 games.
R.J. Umberger scored the game-tying goal in the second period for Columbus, which extended its season-best win streak to five games.
The Blue Jackets also received goals from Antoine Vermette and Chris Clark and they got 21 saves from Mathieu Garon, improving to 8-1-0 on the road this season.
New York earned a point, but remained winless (0-11-3) since October 21. Trent Hunter, Michael Grabner and Frans Nielsen all had two points in the loss.
Midway through the overtime period, Columbus defenseman Kris Russell carried the puck into the zone and ripped a shot on Islanders goaltender Rick DiPietro. Voracek hammered home the rebound at 2:31 for the game-winner.
DiPietro was peppered with 38 shots in the loss, turning aside 34. He made 10 saves in the third period to keep the Islanders in the game.
But New York failed to win in its fourth game under interim head coach Jack Capuano, who took over after Scott Gordon was fired last week. The Islanders are 0-2-2 with Capuano on the bench.
DiPietro made his best save in the first two minutes of the game, spinning around to his right stop a wide-open shot that Voracek was trying to stuff into the net.
The Islanders then opened the scoring midway through the first period on Hunter’s goal, which he wristed off Garon’s shoulder from the left side. But Columbus would have the lead before the period was over.
Derick Brassard threaded a pass down low on the power play to Vermette, who one-timed it into the net to even the score at 1-1 with 6:12 remaining in the period.
Chris Clark gave the Blue Jackets a 2-1 lead, beating DiPietro on a rebound he hammered home just 2:10 after Brassard’s tally.
Grabner evened the game at 2-2 for the Islanders when he scored on a backhand 51 seconds into the second period.
John Tavares made 3-2 New York just 1:33 later, finding himself in the right place at the right time when the puck caromed off the glass and landed in front of the net. Tavares tipped it through Garon’s legs.
Umberger netted the equalizer at 6:46 of the final period and the teams remained knotted through the end of regulation.
Columbus won for just the second time in its last six meetings between the teams…The Blue Jackets snapped a three-game losing streak on Long Island…The Islanders suffered through a 15-game winless streak from November 22 to December 23, 1999, but that drought featured three ties.