Owen Power scored his second goal in as many nights to make it 3-0 at 9:07, finishing a backdoor tap-in off a pass from JJ Peterka.
Thompson extended the lead to 4-0 at 1:10 of the second period. He scored with a backhand in front off a pass from Tuch after Colton Parayko turned the puck over in the neutral zone near the Sabres' blue line.
Ivan Barbashev cut the lead to 4-1 at 4:33 with a spinning backhand near the left hash marks.
Schenn then made it 4-2 at 7:56 when he shot glove side from the top of the left circle on a 4-on-2 rush.
"It was really close I thought to make it 5-0, and it didn't happen and they came back in the game, give credit to them," Buffalo coach Don Granato said. "They fought hard. They are a good hockey team, and the atmosphere got going and you've got to win games and find ways to win games regardless. You've got to be able to handle adversity, adverse situations. I thought our guys through the end battled extremely well even down a man, two men with the goalie pulled. We looked confident and stayed aggressive."
Jordan Kyrou scored 47 seconds into the third period to cut it to 4-3, beating Luukkonen glove side from the top of the right circle.
"We felt good between the second and third, getting two goals and getting ourselves rolling," Krug said. "Obviously, we get one first shift (in the third) and feel good about it, but we came up short."