Teuvo Teravainen scored for the Hurricanes (34-10-7), who are 7-0-3 on their streak. Alex Nedeljkovic made 31 saves.
Hamilton took a pass off the boards from Nedeljkovic in the neutral zone and scored on a backhand. The assist was the rookie goalie's first NHL point.
"It can't get much better than that, aside from scoring yourself," Nedeljkovic said. "It's something I enjoy doing, and it makes our defensemen's lives a lot easier. It was nice to get a chance to get one there in overtime when things are a little bit more open."
Carolina remained two points ahead of the Florida Panthers for first place in the Discover Central Division with two games in hand.
Max Domi scored for Blue Jackets (16-25-11). Elvis Merzlikins made 31 saves.
"I thought we played really well tonight," Columbus coach John Tortorella said. "I thought we played disciplined, we were simple. Playing as groups was really consistent tonight. One of the things we need to improve at is when we do have odd-man rushes, to get more on them. That hurts us a bit."