Brandon Tanev had a goal and two assists, and Carson Soucy and Jaden Schwartz also scored for the expansion Kraken, who had their season-high scoring total. Yanni Gourde and Morgan Geekie each had two assists.
''It's a big vote of confidence for a lot of guys, and it shows our depth of scoring,'' said Appleton, who scored his first goals of the season after he missed the first 11 game with a lower-body injury. ''We've got 12 guys who can put the puck in the back of the net on any given night.''
Chris Driedger made 32 saves as Seattle won for the fourth time in five games and second straight on the road for the first time.
''The commitment level and opportunistic mindset of our team tonight was great,'' Tanev said. ''They gave us a late push, and a couple of late goals. But at the end of the day, we got a great win here for our group.''
Jeff Skinner had two goals for the Sabres, who have lost five in a row at home and six of seven overall. Brett Murray had a goal and an assist, Dylan Cozens also scored, Kyle Okposo had two assists, and Dustin Tokarski stopped 25 shots.
''We didn't have a sense of urgency at the start with respect to details,'' Sabres coach Don Granato said. ''We allowed too much, too easy, and then fought, obviously, the rest of the way as a result.''
Seattle scored the first two short-handed goals in franchise history as part of a three-goal opening period. The Kraken took advantage of turnovers by Buffalo's Rasmus Dahlin on both goals.
''You come into a building and you kind of suck the air out of it when you score goals like that,'' Appleton said.
Gourde outworked Dahlin in the corner before setting up Soucy's slap shot from the high slot 16 seconds into a Sabres power play at 5:47.
Tanev stripped Dahlin and beat him down the ice to knock in the rebound from his own shot 25 seconds after the Sabres gained the man-advantage later with 5:20 left in the first period.
''Those guys have the green light to go when they can without creating a ton of risk,'' Kraken coach Dave Hakstol said. ''It was a real good read to jump the first one. And the second is just pure effort all the way up the ice.''
McCann scored off a rebound to make it 3-0 with 56 seconds remaining in the period.
After Murray got his first NHL goal at 1:53 of the second, Geekie made a one-armed backhand pass from behind the net to set up McCann's second goal and restore the three-goal lead.
Appleton gave the Kraken a 5-2 lead 42 seconds after Skinner's power-play goal in the closing minutes of the second.
Skinner scored again 37 seconds into the third period to pull the Sabres within two again.
''We definitely had opportunities,'' Skinner said. ''We just didn't seem to be able to sustain any type of momentum.''
Schwartz put the Kraken back ahead by three with 6:16 remaining.
Cozens deflected Okposo's shot past Driedger to make it 6-4 with 1:33 left before Appleton scored into the empty net with 25 seconds to go.
Kraken: Leading scorer F Jordan Eberle left in the third period with a lower-body injury and did not return. Hakstol had no immediate update on Eberle's status and said he will be evaluated on Tuesday.
Sabres: F Casey Mittelstadt (upper body) has been cleared for contact in practice and could return on the coming road trip, Granato said. Mittelstadt was Buffalo's top-line center before getting hurt in the opener, and has missed 21 games. . F Alex Tuch (shoulder) skated in a non-contact jersey for the first time since he was acquired from the Vegas Golden Knights in a trade for Jack Eichel on Nov. 4. Granato said Tuch is still ''weeks away'' from playing. . D Jacob Bryson was scratched with an undisclosed nagging injury.
NOTES: Kraken D Will Borgen recorded his first NHL point on Appleton's first goal. Seattle's selection from Buffalo in the expansion draft became the 33rd player to get his first point against the team that drafted him. . Gourde's assist gave him 200 career points. . Dahlin got his 100th assist on Skinner's first goal. . Will Butcher saved a goal for Buffalo in the second period, lunging with his stick behind Tokarski to keep the puck from crossing the line after it dribbled through the goalie's pads. . The Sabres were the last team to score two short-handed goals in the same period in a win against the Flyers on March 31.
Kraken: Close a four-game road trip at Detroit on Wednesday.
Sabres: At Florida on Thursday.
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