The Sabres have come from behind to win six times during their streak.
“Guys don’t give up and sort of have that belief that you can come back,” Skinner said.
Casey Mittelstadt also scored, and Carter Hutton made 31 saves in his seventh straight victory.
Brendan Gallagher and Andrew Shaw scored for the Canadiens, who have lost three straight. Phillip Danault had two assists, and Antti Niemi stopped 37 shots.
“We lost a big point,” Canadiens coach Claude Julien said. “We minimized the scoring chances against a team that’s doing well. We were in a good spot until the final few minutes.”
Skinner scored both of his goals on rebound chances near the front of the net. The top-line winger acquired in an offseason trade with Carolina has 17 goals, tied with David Pastrnak for the league lead.
“He has a dog-on-a-bone mentality,” Sabres coach Phil Housley said. “Any loose puck or retrieval, he was going to get on it.”
Skinner got the winning goal late in a 4-on-3 power play after he drew a slashing penalty on Montreal’s Max Domi. Skinner knocked in a rebound while falling down between the faceoff circles following Niemi’s saves on shots by Jack Eichel and Rasmus Ristolainen.
Skinner tied the game with 2:26 left in regulation. Gathering the rebound of Zach Bogosian’s shot in the right circle, Skinner flung a backhand by a sliding Niemi.
Buffalo’s Jake McCabe then hit the post on a slap shot with 29 seconds left in regulation.
Shaw’s power-play goal gave Montreal a 2-1 lead 8:18 into the third period. Danault won a faceoff in the Sabres’ zone and Shaw deflected David Schlemko’s slap shot past Hutton five seconds after Jason Pominville went to penalty box for holding.
The Canadiens had tied the game late in the second when Danault set up Gallagher on a 2-on-1 for his 11th of the season on a wrist shot from the right circle.
Gallagher had a goal disallowed about five minutes earlier when video replays confirmed he kicked the puck into the net.
Having allowed 10 goals in their previous two losses, the Canadiens were pleased with their improvement on defense.
“The positive point from tonight is we had a great defensive game,” Danault said. “Nemo was solid in net and our D was playing well, too.”
Mittelstadt scored off a rebound with 7:21 remaining in the opening period. Conor Sheary deflected McCabe’s shot from the point off the right post and Mittelstadt reached in from the right edge of the crease to sweep the puck across the goal line.
NOTES: Domi had a 12-game point streak snapped. It was the longest by a Canadiens player since Pierre Turgeon had a 13-game streak in April 1995. … Sabres D Marco Scandella returned after missing one game with a lower-body injury. … Canadiens F Matthew Peca moved back into the lineup, replacing Charles Hudon at left wing on the third line. Peca centered Montreal’s fourth line before being scratched for Wednesday’s 5-2 loss in New Jersey. … D Brett Kulak made his Canadiens debut after being called up from the minors on Thursday. Kulak and D Karl Alzner entered the lineup in place of Mike Reilly and Xavier Ouellet.
Canadiens: Home against the Boston Bruins on Saturday.
Sabres: At Detroit on Saturday
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