Kevin Stenlund scored in regulation for the Blue Jackets. Oliver Bjorkstrand assisted on all three goals.
Once Jones took control of the puck on the last sequence, he chose not to give it up.
''Crossing the blue line, I thought (Carolina defenseman Dougie) Hamilton was in a pretty good spot,'' Jones said. ''I looked pass first, and when I got to the top of the circle I was really thinking shot. With the ice not being the greatest, I just decided to put one on net.''
Sebastian Aho scored twice for the Hurricanes, who lost their second straight after an eight-game winning streak.
Columbus goalie Joonas Korpisalo stopped 25 shots, including Martin Necas' attempt off an overtime breakaway.
Alex Nedeljkovic made 25 saves for Carolina in the first of four consecutive meetings between the teams. The teams play again Saturday.
Jones opened and closed the scoring, giving him three goals this season.
''We needed someone to take control of the game for us,'' Columbus coach John Tortorella said. ''I thought he stood up and said I'm going to be the guy.''
Jones is the franchise career leader in points among defensemen. He never had a goal in 27 previous games against the Hurricanes.
''I was just trying to be aggressive,'' Jones said. ''I want to get that in my game a little bit more.''
The Hurricanes recovered from a rough start, when the Blue Jackets had 14 of the game's first 18 shots.
''We did it in spurts the rest of the way,'' Carolina coach Rod Brind'Amour said. ''It was a pretty even game after the first period.''
Aho's first goal came 51 seconds into the second period. His second goal came on a power play, though the shot was unleashed not too far from the spot of his first tally on the left side of the net.
Aho pulled even with Nino Niederreiter, who had scored in each of the past two games, and injured Vincent Trocheck for the team lead in goals with 13.
Stenlund, who wasn't in the team's original lineup, tied the game with 2:10 remaining in the second period. It was his fifth goal of the season.
It was the fourth consecutive Columbus game to go beyond regulation. It marked the 18th one-goal game for the Blue Jackets, who are 9-2-7 in those games.
The Hurricanes were limited to four third-period shots.
''I thought we really settled down,'' Tortorella said. ''I don't think we even gave them a chance in the third period.''
THAT WORKED OUT
Stenlund had gone seven consecutive games without a point and was set to be a healthy scratch before the lineup change. He replaced Mikhail Grigorenko, who was out with an illness not related to COVID.
Stenlund, who has scored in both of the team's games in Raleigh this season, has logged more than 12 minutes only once in his last six outings. Still, he showed signs of the types of contributions needed.
''I just want to notice (Stenlund),'' Tortorella said about the center. ''I'm not worried about mistakes, but I can't have him blend in. That's what I thought was happening with his game.''
The Columbus roster was also affected by putting center Emil Bemstrom on injured reserve because of a lower-body injury sustained in Wednesday's practice.
RIGHT ON TIME
Korpisalo had to make as many saves in the first four minutes of overtime as he did in the entire third period. The most challenging one came when Necas skated in on what amounted to a long breakaway.
''He had a lot of time. I had a lot of time to set myself up,'' Korpisalo said of assessing the situation. ''It's my job to stop the pucks.''
Korpisalo has run hot and cold against the Hurricanes. In two victories, he allowed two goals in each game. In two losses, he yielded 11 goals across five periods.
Hamilton has a 10-game points streak after his assist on Aho's second goal. That's one game shy of the franchise record for a defenseman.
During the current streak, Hamilton has just one game with more than one point. He holds the NHL's longest active points streak.
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