Chris Kreider and Ryan Poehling also scored for the Ducks (27-21-3), who had lost nine straight (0-8-1) before their current streak began on Jan. 13. Lukas Dostal made 20 saves.
Jared McCann and Jaden Schwartz scored for the Kraken (22-19-9), who have lost seven of nine (2-5-2). Philipp Grubauer made 27 saves.
Gauthier gave Anaheim a 1-0 lead at 1:02 of the first period, taking a pass from Jeffrey Viel at the Seattle blue line, speeding around defenseman Vince Dunn and snapping a shot inside the left post from the bottom of the right circle.
Poehling extended it to 2-0 with a short-handed goal at 15:24. Ian Moore backhanded a loose puck out of the Anaheim zone, springing Poehling on a breakaway. Poehling cut from left to right, deked, and chipped it over Grubauer’s right pad.
McCann cut it to 2-1 at 1:55 of the second period, taking Jordan Eberle’s feed off a 3-on-2 rush and firing a wrist shot from the slot over Dostal’s right shoulder.
Kreider’s power-play goal 2:05 later made it 3-1 at 4:00 when he slapped Gauthier’s rebound into an open net from the top of the crease.
Grubauer used a poke check to stop Jansen Harkins on a penalty shot at 8:00 after Ryan Lindgren held Harkins on a breakaway.
Schwartz brought Seattle within 3-2 at 1:54 of the third period, lunging at the top of the crease and redirecting Shane Wright’s feed from the top of the slot into an open net.
Mintyukov then banked a shot off the side boards from the defensive zone and into an empty net at 18:48 for the 4-2 final.
