Sebastian Aho scored twice, Micheal Ferland had a goal and two assists, and Curtis McElhinney made 30 saves for the Hurricanes (21-18-5), who have won six of their past seven games and defeated the Sabres for the seventh straight time.
"We were very fortunate," Carolina coach Rod Brind'Amour said. "We didn't play well at all, but we played better as the game went on. We played hard, but execution wasn't good and we got a couple breaks."
WATCH: [All Sabres vs. Hurricanes highlights]
Skinner scored his 30th goal of the season, and Carter Hutton made 26 saves for Buffalo (23-15-6), which is 3-6-1 in its past 10 games.
"It's nice to contribute, get an early power-play one there," said Skinner, who was traded for forward Cliff Pu and three draft picks Aug. 2. "We maybe gave them a few too many rushes than we should have."