Phil Kessel scored for the first time in 18 games and had an assist for the Coyotes (12-31-4), who had lost their previous two games.
Colin Blackwell and Calle Jarnkrok scored, and Philipp Grubauer made 22 saves for the Kraken (15-28-4), who are 0-2-0 against Arizona.
"We weren't sharp, we weren't clean with the puck," Kraken coach Dave Hakstol said. "In reality, each of their three goals came off our sticks. … The rust showed, we're not making an excuse, but we weren't sharp when we didn't have the puck. That area of our game was not at the level it needed to be. Without the puck we weren't connecting as much as we are when it's going well."
Kessel gave Arizona a 1-0 lead at 4:07 of the first period after he intercepted an errant pass from Adam Larsson deep in the Seattle end, turned with the puck and slid it past Grubauer.
"It's no secret it's always better to play with the lead," Coyotes forward Alex Galchenyuk said. "When Kessel found that goal, me and [Lawson Crouse] were on the bench and saying 'he's feeling it right now'. He scored a big goal and that got the bench fired up. When you come into a game and you want to bounce back and you get on the lead right away, it's a completely different game."
The Coyotes made it 2-0 at 14:51 of the second period after Galchenyuk made a stretch pass to Nick Schmaltz, who scored on a wrist shot from the left circle.