Vince Dunn tied the game 3-3 with 53 seconds remaining in the third period for Seattle, sending a wrist shot from the left point through traffic and past Kevin Lankinen's glove, forcing overtime.
Lankinen made 13 saves, plus three more in the shootout, in relief of Thatcher Demko, who stopped 11 of 12 shots before exiting with back spasms at 7:49 of the second period, for the Canucks (18-11-8), who had lost their previous two.
Matty Beniers scored for the third game in a row for the Kraken (17-20-2), who had won their previous two games, including a 5-4 comeback overtime win at the Canucks on Saturday. Philipp Grubauer made 19 saves.
Seattle rallied from down two goals in the third period after coming back from down three goals against Vancouver on Saturday.
Beniers cut it to 3-2 with a power-play goal at 9:05 of the third, one-timing a Shane Wright pass in the slot over Lankinen's shoulder.
Dunn, who scored in overtime on Saturday, then tied it with Grubauer pulled for an extra attacker.
Chandler Stephenson gave the Kraken a 1-0 lead at 1:52 of the first period with a snap shot off a rush from the left circle that squeezed under Demko's blocker.
Max Sasson tied it 1-1 at 13:17 when a Nils Hoglander shot from the top of the right circle got partially blocked and caromed off Danton Heinen's skate to Sasson at the top of the crease. Sasson slapped it past Grubauer's right pad.
Conor Garland gave Vancouver a 2-1 lead with a breakaway goal at 7:49 of the second period. Phillip Di Giuseppe found Garland with a stretch pass at the blue line, and he deked to his forehand and slipped the puck around Grubauer's left skate.
Tyler Myers pushed it to 3-1 at 5:35 of the third period, taking a Miller feed at the top of the right circle and firing a wrist shot past Grubauer's blocker.