Alex Nedeljkovic made 19 saves for his second NHL shutout.
Jesper Fast had a goal and an assist, and Sebastian Aho had two assists for the Hurricanes (21-7-3), who lost the first two of the four-game series against the Blue Jackets at home, 3-2 in overtime Thursday and 3-2 in the shootout Saturday.
Hamilton has two goals and 12 assists during his point streak and passed Hockey Hall of Famer Mark Howe for the longest by a defenseman in Hurricanes/Hartford Whalers history. It is the longest active streak in the NHL and one game shy of Toronto Maple Leafs forward Auston Matthews' from Jan. 24-Feb. 20 for the longest this season.
"I don't think about it too much," Hamilton said. "It's just trying to take it day by day and one game at a time. I know it's a cliché, but with the schedule right now, it's just kind of focus on one game.
"I'm lucky to play with great players and guys making good plays."
Joonas Korpisalo made 25 saves for the Blue Jackets (13-13-7), who lost in regulation for the first time in six games (3-1-2).
"They checked tonight, and we couldn't get through it," Columbus coach John Tortorella said. "It's a big part of what they do, and tonight we had trouble getting through it."
The teams will conclude the four-game series here Thursday.
Hurricanes coach Rod Brind'Amour said he thought they played well in the two losses to the Blue Jackets.
"I felt really good about our games," he said. "We had one iffy period out of the whole set so far, the first game, first period, so it was a solid effort all the way around, and we got some nice plays but we didn't cash in. But tonight they did, and I thought for two periods, especially, we just kind of controlled the game that we had to win."