Curtis McElhinney made 35 saves for the Hurricanes (39-25-7), who lead the Columbus Blue Jackets by one point and the Montreal Canadiens by four for the first wild card into the Stanley Cup Playoffs from the Eastern Conference.
Carolina is 8-2-1 in its past 11 games and trails the Pittsburgh Penguins by two points in the division. They play Tuesday.
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"It feels good," McElhinney said. "Everybody's doing their job. It's a critical time of year, and it's been fun being in that conversation and keep picking up points. Huge effort by everyone."
Jeff Skinner scored for the first time in 14 games for the Sabres (30-32-9), who had been shut out in their three previous games. Buffalo has lost seven in a row and is 2-11-2 in the past 15 games. Linus Ullmark made 25 saves.
Skinner made it 1-0 at 2:18 of the first period when he brought the puck from behind the net and tucked it between McElhinney's legs. His 37th goal tied his NHL career high, set with Carolina two seasons ago.
"When you're having trouble putting one in, I think sometimes you need to get a bounce or a lucky one," Skinner said. "We had some pretty good looks after that and again just couldn't seem to get that second one."
Lucas Wallmark tied it 1-1 at 13:52. After Jordan Martinook's shot trickled through Ullmark's pads, Wallmark moved into the crease to tap in the loose puck.