Canadiens rookie sensation Ivan Demidov tied the game with under three minutes left in the third period to force the extra session.
Alex Newhook and Kirby Dach also scored for Montreal. Samuel Montembeault made 18 saves in the winning effort. The Canadiens ran their winning streak to three games as they launched a four-game homestand.
Jaden Schwartz, Jani Nyman, Jamie Oleksiak and Jared McCann also scored for the Kraken, who dropped their first game of the season and the opener of a six-game road trip. Joey Daccord stopped 17 shots.
The Canadiens exacted revenge on Seattle, which swept the two-game season series last season, including an 8-2 drubbing on home ice last October.
The Canadiens win was the culmination of a night filled with celebrations surrounding Montrealâ€s home opener.
Pre-game ceremonies were highlighted by lengthy ovations for Canadiens head coach Martin St. Louis, Demidov, and reigning Calder Trophy winner Lane Hutson, who signed an eight-year, $70.8 million contract extension on Monday.
Canadiens: Newhook scored his first goal of the season in his 300th career NHL game. The goal was assisted by defenceman Alexandre Carrier, who also celebrated his 300th game on Tuesday.
Kraken: McCann, meanwhile, scored in his third straight game to start the season. The 29-year-old, who also collected an assist in the game, has four points over the stretch.
It took less than five minutes for the Canadiens to open the scoring as Newhook, positioned at the far post, tapped in a perfectly-placed pass from Demidov behind Daccord on just Montrealâ€s second shot on goal.
Caufield scored in a fourth straight Canadiens home opener. The 24-year-old has five goals across those four opening-night contests.
Kraken: Visit the Ottawa Senators on Thursday.
Canadiens: Host the Nashville Predators on Thursday.
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