“It plays a big role in our wins when we get that secondary scoring going,” said Buffalo captain Brian Gionta. “Foligno early on, Larsson with a big one to go ahead. Stuff like that is key.”
Gionta had an empty-net goal with 13 seconds left to play and Jamie McGinn also scored for the Sabres (21-26-4), who moved out of last place in the Atlantic Division, one point ahead of Toronto, which holds two games in hand.
Buffalo, after its first game since the all-star break, is 6-4-0 in its last 10 games.
They trailed 2-1 going into the third period, but outskated Montreal the rest of the way.
"We just stuck with it," said McGinn. "We stayed positive.
"We got shots to the net and fortunately we found the back of the net."
The Sabres' third period outburst, aided by poor defending by the Canadiens, had the Bell Centre crowd booing. The Canadiens were coming off a 4-2 loss Tuesday night in Philadelphia, so fatigue may have been a factor, but they were in no mood for excuses.
The Canadiens opened the season on a 19-4-3 tear but are 5-20-1 since then and have fallen out of the playoff picture.
"I don't know what to say," said Weise. "It's the same thing every game.
"We made a lot of turnovers. There's no excuse for that. But we've got to find a way."
Weise said he understands that fans who thought the Canadiens would contend for a Stanley Cup this season grow angrier with each loss as the team struggles without injured star goalie Carey Price.
"We feel bad for them," said Weise. "We're laying it on the line out there.
"It's not from a lack of effort. The fans pay a lot of money to come and watch games and we respect them if they want to boo or not. That's their prerogative. But we're trying our best out there."
Montreal outshot the Sabres 35-32.
Weise tied it on a power play 3:19 into the second when he was at the edge of the crease to take a feed from Max Pacioretty and tap in his 12th of the season.
McGinn tied it 2-2 on a power play 7:34 into the third period when he was at the edge of the crease to tip in a diagonal feed from Rasmus Ristolainen.
Notes -- Normally, the first home game of February sees the Canadiens award a player of the month honour for January. But three players tied for top spot -- Lars Eller, Brendan Gallagher and Max Pacioretty -- and tie-breaking system couldn't settle it, so their points will carry over to next month. That they went 3-7-1 in January meant fewer than usual stars were awarded.