Skinner gave the Sabres a 3-2 lead at 16:29 off a backhand pass from Jack Eichel, who scored an empty-net goal at 19:35 to make it 4-2.
Eichel had two goals and two assists, Linus Ullmark made 35 saves, and Sam Reinhart had three assists for Buffalo (20-9-5), which has a point in four straight games (3-0-1). Rasmus Dahlin had two assists.
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"It's always special coming back home, having a lot of family and friends here," said Eichel, who's from Lynnfield, Massachusetts. "It's awesome that we played such a good game as a group and we just stuck with it. Obviously, it wasn't the outcome we wanted [Saturday] night (4-3 shootout loss to Washington Capitals), probably wanted two points, could've had it. But it's great to come in here, in less than 24 hours, get two points and move on."