Chris Campoli, Scott Gomez and Tomas Kaberle scored in regulation to help the Canadiens (24-25-10) win their third straight road game and improve to 5-1-1 in their past seven overall. The win gives the 11th-place Canadiens 58 points, six behind eighth-place Toronto.
"We've got to continue to go here. We don't have time to look at it and reflect," defenseman P.K. Subban said after playing 28:48 in a game played a few hours after the Canadiens sent veteran defenseman Hall Gill to Nashville. "We've got a long way to go."
The Sabres have an even longer path -- The single point leaves Buffalo last in the East with 55.
"Obviously, I'm very disappointed, embarrassed," Sabres coach Lindy Ruff said. "We've dealt with a lot, but to be where we're at is a big disappointment."
Tyler Ennis, Tyler Myers and Robyn Regehr scored for Buffalo, which was coming off a 7-2 loss at Philadelphia on Thursday. The Sabres have dropped four in a row, though they got a point after Ennis forced overtime by scoring with 8:05 left in regulation.
The shootout didn't last long. After Price denied Brad Boyes, Pacioretty scored on the Canadiens' first attempt. Price stopped Jason Pominville and Desharnais sealed it by driving across the front of net before stuffing a shot just inside the left post past Ryan Miller's pad.
"Any way you win it, obviously, those are extra points that we desperately want and need," interim coach Randy Cunneyworth said. "I think we deserved it tonight. I'm happy for the boys. It's good to get the reward."
Price also made 27 saves through 65 minutes as the Canadiens snapped a 0-3-3 skid against the Sabres that included three losses this season in Montreal.
One night after blowing a 2-0 lead in Philadelphia, the Sabres twice were unable to hold one-goal leads in the opening period.
Campoli gave the Canadiens their first lead, breaking a 2-2 tie 11:28 into the second period. The goal came on the return rush after Buffalo's Zack Kassian failed to get a shot off on an odd-man rush. Campoli got the puck at the right boards and skated unchecked to the middle before lifting a shot into the top left corner over Miller, who was down after Sabres defenseman Mike Weber shoved Gomez into the goalie.
Ville Leino, who had two assists, set up Ennis' tying goal by outworking Campoli behind the net and firing a bad-angle shot that hit Price's stick. The puck squirted into the slot, where Ennis fired it into the open left side of the net.
Lack of discipline has also troubled Buffalo -- Montreal's first two goals came at the end of power plays.
Kaberle converted Desharnais' feed through the crease to tie the game at 1-1 just one second after Buffalo's Thomas Vanek finished serving a cross-checking penalty. Gomez made it 2-2 with 14 seconds left in the period, a second before Nathan Gerbe's hooking penalty expired.
"Right now, pucks are going off sticks and bouncing off the ice, deflecting top corner, we can’t keep the puck out of our net killing penalties and we’re usually a good penalty-killing team," Ruff said.
Myers agreed that discipline has to improve for the Sabres to get back in the race.
"Those are penalties we can't take and it's killed us the last two games so we've got a lot to figure out before we start winning games here," said Myers, who picked up his 100th career point while also playing in his 200th career game. "For the most part of that game, other than our penalty kill, I thought we dominated the play for the most part. We worked really hard down low. We generated some chances. Just once again, penalties killed us."
Ruff sat both Vanek and Gerbe for extended stretches after their penalties.
"Yeah, it was a message," Ruff acknowledged. "It's an issue that has to be dealt with."
Material from team media and wire services was used in this report