Marcus Johansson scored the go-ahead goal in the third period for the Wild (16-9-5), who had lost three of their previous four (1-2-1) after their seven-game win streak ended with a 3-2 shootout loss to the Buffalo Sabres on Nov. 29.
Minnesota concluded its four-game road trip with 2-2-0. Filip Gustavsson had 23 saves.
Jordan Eberle had a goal for the Kraken (11-10-6), who have lost six straight (0-5-1). Philipp Grubauer had 25 saves.
Eriksson Ek gave Minnesota a 1-0 lead at 1:18 of the second period, taking Matt Boldy’s feed from below the goal line and tapping it through Grubauer’s five-hole from the low slot.
Eberle tied it 1-1 with a power-play goal at 6:48. Following a face-off win by Chandler Stephenson, Jared McCann collected the puck and sent a cross-ice pass to Stephenson in the right face-off circle, where he then connected with Eberle on a backdoor pass for the goal.
Minnesota forward Mats Zuccarello left the game after taking a hit from Seattle defenseman Vince Dunn at 14:59 of the first period. Dunn was originally given a five-minute major penalty for the hit but it was rescinded after an official review.
Johansson put the Wild back up 2-1 at 8:12 of the third period. Eriksson Ek threw a backhander at the net from the right boards and Johansson tipped it between his legs past Grubauer.
Seattle forward Tye Kartye appeared to have evened the game 2-2 just nine seconds later at 8:21, but it was ruled that he batted the puck out of the air above the crossbar.
Kirill Kaprizov and Vladimir Tarasenko each added empty-netters at 18:45 and 19:00 for the 4-1 final.