Tyler Johnson tied it 4-4 from the slot at 12:57 before Jason Dickinson put Chicago in front 5-4 with a shot blocker side from the right circle at 13:10.
"Well, I just think it's the compete [level] on the team," Johnson said. "I think everyone in here just keeps working hard regardless of the score. It's what we've talked about from Day One. It's just playing our game doing what we need to do, control what we can control and just keep going."
Johnson scored two goals, and Alex Stalock made 30 saves for the Blackhawks (3-2-0), who have rallied from down 2-0 to win three straight games for the first time in their history.
"Definitely impressive," Chicago coach Luke Richardson said. "As the game went along, we played better, and when it really counted at the end, we played hard and they played for each other. They're really becoming a group in there, and it's nice to see. But, just mentioned to them after the game that we dodged a bullet for sure."
Martin Jones made 22 saves for the Kraken (2-3-2), who were 0-for-4 on the power play and won 31 percent of their face-offs (18-for-59).
"Disappointing loss," Seattle coach Dave Hakstol said. "We did a lot of things that will end up getting you beat on the road. You can look at face-offs, specialty teams early, including a short-handed goal early that really feeds them and gives them life in this hockey game. Down to most importantly, just the way we checked and played without the puck in the last 40-45 minutes of this hockey game."