David Rittich made 27 saves for the Jets.
John Hayden and Jared McCann scored for Seattle.
Philipp Grubauer turned aside 37 shots for the Kraken, who dropped to 30-19-5.
There was no scoring in the first period.
Blake Wheeler opened the scoring just over seven minutes into the second period when he took a pass from Nikolaj Ehlers from the end boards before skating in front of Grubauer and cutting back to beat him with a forehand shot.
The goal was his 15th of the season.
John Hayden evened the contest at 13:20 when he drove the net and got his stick down on a hard pass from Morgan Geekie, who fired a pass from the left side boards.
The goal was his 2nd of the season.
Jared McCann gave Seattle the lead with a power play marker at 19:33.
With Pierre-Luc Dubois off for interference, McCann's shot from the point careened off the skates of both Dylan DeMelo and Mason Appleton before sliding past Rittich to make it 2-1 Kraken.
The goal was his 25th of the season.
Pierre-Luc Dubois tied it up 9:39 into the third when he converted a Josh Morrissey feed, banking the puck off of Seattle defenceman Vince Dunn and past Grubauer to make it 2-2.
The goal was his 23rd of the season.
Winnipeg got a chance to grab a late lead with just over five minutes remaining in the third when Oliver Bjorkstrand took a slashing penalty but were unable to score.
The game went to overtime.
There was no scoring in overtime and the game went to a shootout.
SEATTLE-Donato (miss), Eberle (miss) WINNIPEG-Scheifele (score), Connor (miss), Dubois (score) Both clubs see action next on Thursday as Winnipeg visits Columbus while Seattle hosts Philadelphia.
SHOTS-SEATTLE 29 WINNIPEG 40
ATTENDANCE-14,237
NOTES-Josh Morrissey set a new record for assists for a Jet defenceman with his assist on Pierre-Luc Dubois' third period marker.
