Alex Wennberg and Brandon Tanev also scored, and Philipp Grubauer made 21 saves for the Kraken (36-21-6), who swept a four-game road trip.
Seattle is in third place in the Pacific Division, two points behind the Los Angeles Kings for second, and two ahead of the Edmonton Oilers.
"We're happy with the two points," Kraken coach Dave Hakstol said. "We had to really stay with it, had to get a little bit better throughout the game. I got a ton of respect for [the Avalanche]. They're outstanding. They're playing on a back-to-back, so we had to find a way to take advantage of that, just in terms of overall energy as you go through the hockey game."
Nathan MacKinnon scored his 25th goal of the season, and Georgiev made 32 saves for the Avalanche (34-21-6), who have lost three straight.
Colorado, which lost 7-5 to the New Jersey Devils on Wednesday and 7-3 to the Dallas Stars on Saturday, are third in the Central Division, four points behind the Minnesota Wild.
"I didn't like our game tonight again," Avalanche coach Jared Bednar said. "You could say, 'Well it was improved from giving up seven,' but I would hope so. It was tough sledding tonight energy-wise. Mentally, it looked like we were fried. I didn't think our top guys had a very good night at all."