Brandon Tanev had a goal and two assists, and Morgan Geekie and Yanni Gourde each had two assists for the Kraken (8-13-1), who have won four of their past five games. Chris Driedger made 32 saves.
"The more you win, the more you trust the system," Appleton said. "Whether that is how your line plays, how the team plays, whatever that is, a win gives you belief in many different ways. I thought we did a good job for most of tonight's game. We hit a couple walls here and there. But at the end of the night, we got the points. And that's what matters in this league."
Jeff Skinner scored twice, Brett Murray had a goal and an assist, and Kyle Okposo had two assists for the Sabres (8-11-3). Dustin Tokarski made 25 saves.
"There were some good things in the game, but we didn't have a sense of urgency at the start with respect to details," Buffalo coach Don Granato said. "That was obvious. We allowed too much, too easy, and then fought obviously the rest of the way as a result."
Carson Soucy scored the first shorthanded goal in Kraken history for a 1-0 lead at 5:47 of the first period. Gourde picked up a loose puck after Sabres defenseman Rasmus Dahlin fell behind the Buffalo net and passed to Soucy in the high slot.
Tanev scored a second shorthanded goal when he poked the puck away from Dahlin at the Seattle blue line and held him off to score on the rebound of his own shot to make it 2-0 at 14:40.
"That's just good, hard work," Kraken coach Dave Hakstol said. "Good instincts on the first one, 'Gourdie' gets up ice and creates a turnover. He could kind of sense that, and he got up and got on top of it, and the second one is just great individual effort."