Alex Wennberg scored twice, and Daniel Sprong had two assists for Seattle (6-4-2), which concludes a three-game road trip Saturday at the Pittsburgh Penguins.
"It was just straight up 60 minutes of hockey," Kraken coach Dave Hakstol said. "We just wanted to play a real good road game in a tough building. This building can be where momentum can get rolling, so we wanted to make sure we were ready to play a good, smart road game. Make sure we were skating, make sure we were competing in all the little areas of the game, puck battles and everything else."
Marc-Andre Fleury made 19 saves for the Wild (5-5-1), who won their previous two games.
"I don't know. I'm not going to try to make excuses," Minnesota coach Dean Evason said. "We just flat out didn't have the energy level that we needed to play here tonight."
Morgan Geekie made it 1-0 at 5:02 of the second period with a deflection of Sprong's shot from the half-wall.
Geekie has scored in three straight games and has five points (four goals, one assist) in his past six.
"I just try to stick to my game for the most part," Geekie said. "I've got a couple of good linemates helping me out. … I'm just trying to be in the right spot at the right time and create offense."
Jamie Oleksiak extended the lead 2-0 at 11:34 with a one-timer, and Wennberg made it 3-0 at 14:47 on the power play.
"They came out hot," Wild forward Matt Boldy said. "They were all over us. Their D had really good gaps and I don't think we were doing the right things early; [we were] trying to be a little too cute with it, myself included. We just got away from our game because we were trying to make too many plays."