Jared McCann and Jordan Eberle each had a goal and two assists, Matty Beniers had a goal and an assist and Philipp Grubauer made 27 saves for the Kraken (44-26-8), who finished 30th last season (27-49-6), their first in the NHL.
"It's unbelievable, it's hard to put into words, the excitement, the growth, the steps we've taken and the way we've come together," Seattle forward Jaden Schwartz said. "It's obviously exciting … everyone's just really fired up that we're in in the playoffs. It's a dream come true for us, and to be able to do in our second year is pretty special."
The win moved the Kraken seven points ahead of the Winnipeg Jets and Calgary Flames for the first wild card into the playoffs from the Western Conference.
"This group believed in it and pushed through that finish line, and I don't believe they're done yet," Seattle coach Dave Hakstol said. "Points are still valuable to us in terms of positioning and how you're feeling going into the playoffs. We'll find out who [we play] and then go to work. That's just what the group does. Go to work."
Barrett Hayton and Laurent Dauphin scored, and Karel Vejmelka made 30 saves for the Coyotes (27-39-13), who have lost nine in a row (0-7-2), including 8-1 at Seattle on Monday. Arizona has been outscored 24-7 in its past four games.
"I don't think we generated a lot in the first and we took a little bit of time to get our offense figured," Arizona coach Andre Tourigny said. "I think we generated enough in the second and third periods. We had [two] power plays, but we couldn't score a killer goal at the right time."
The Kraken scored in the final minute of the first period and the first minute of the second period to take a 2-0 lead.
McCann made it 1-0 at 19:36 of the first after Beniers won a puck battle behind the net and passed to Eberle, who fed McCann for a tap-in. McCann scored two goals Monday and has 38 this season.
"We've got to win. We've got to win to get into the playoffs," he said. "We had the opportunity to do that tonight, and we did it. We rose to the occasion."