Skinner narrowed it to 3-2 at 3:43, scoring from the left circle off a pass from Thompson, who toe-dragged Ekman-Larsson to make the play.
J.T. Miller responded for Vancouver on the power play to make it 4-2 at 7:13, scoring glove side from the high slot off a face-off win by Horvat, who added another power-play goal on a breakaway following a bad line change by the Sabres to make it 5-2 at 8:25.
"We've got a pretty good power play, so any time we can get a power-play opportunity, we hopefully try to take advantage of it," Canucks coach Bruce Boudreau said.
Tuch cut it to 5-3 at 11:12 when he redirected Owen Power's shot from above the left circle.
"I think guys in here are really hard on themselves," Tuch said. "That's good to keep yourself accountable, but you also have to continue to try to work and play your game and not let it get into your head. I think that's something we have to learn as a group. … Bounce back a little quicker. We've done it in the past, we've done it this year, we've just got to get back to it."