Eric Robinson scored, and Elvis Merzlikins stopped 19 shots for his second win for the Blue Jackets, who are off to a 2-0-0 start.
''I thought we were a lot more plugged into this game,'' Blue Jackets coach Brad Larsen said. ''It was a grind, but structurally we were better in a couple of areas we addressed as a group. You had to fight for your ice out there.''
Brandon Tanev scored for Seattle. Philipp Grubauer made 23 saves.
The game was scoreless until Tanev beat Merzlikins at 14:37 of the second period. It was Tanev's team-leading third goal of the season, and he gave the Kraken their first 1-0 lead.
Robinson pulled Columbus even at 10:07 of the third, scoring high over Grubauer. Gregory Hofmann picked up the assist, his first NHL point.
In the 3-on-3 overtime, Laine fired a laser from the right circle, giving Columbus its first overtime win on the season.
''It felt awesome,'' Laine said. ''It's always nice to get the OT winner, but here seeing the fans for the first time when I score like this, it was a good feeling.''
Grubauer, a Vezina Trophy finalist in 2020-21, started his third straight game since heading West from the Colorado Avalanche.
''Obviously it's not the result we wanted,'' Tanev said. ''These are important points early on in the season. You take some good away from that game. There's some stuff we didn't like, but at the end of the day we come out here and get as many points as we can.
''Ultimately it's a learning experience for our group, and we'll be moving on from this.''
Seattle plays at Philadelphia on Monday.
Columbus plays at Detroit on Tuesday.
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