Pacioretty's goal was the 100th of his career. The Canadiens earned their third win in a row and the sixth in seven games -- a stretch that included a 2-0 win in Buffalo on March 16.
"Mentally, the emotional high to come back and get motivated for a game against the Buffalo Sabres was the toughest part," Briere said. "We were a little sloppy in the first period, no doubt about it, but it got better as the game went on."
The Sabres have one win in their past 10 games. They played their fourth game of a five-game road trip that ends Thursday in Nashville. Their top player was goalie Matt Hackett, who made 33 saves in his second start of the season.
The Canadiens had played three games in four nights, including a 4-3 victory in Toronto on Saturday and a win against the rival Bruins in Boston on Monday night.
With eight regular season games to play, they are two points up on Tampa Bay for second place in the Atlantic Division, but the Lightning have two games in hand.
"This is a very important time for us," Price said after his fifth shutout of the season and 24th of his career. "Obviously, everybody's trying to make the playoffs and to be able to pick up points against divisional teams and play well -- it's definitely a confidence-builder."
The win in Boston was costly as two fourth line players left with injuries.
Coach Michel Therrien said Dale Weise, who was checked from behind into the boards, has an upper-body injury and will be out for two to three weeks.
Therrien said Travis Moen, who jumped to Weise's defense and got rocked by a punch from Boston's Kevan Miller, "feels better" but has a concussion and will miss at least a week.
They may have had the most jump on a team that looked short on energy to start the game.
Through two scoreless periods, the loudest cheers from the Bell Centre fans were for a sharp Price save on Matt D'Agostini during a Sabres power play and when Olympic moguls gold medalist Alex Bilodeau was shown on the scoreboard screen.
Montreal broke the scoreless tie on a rush after a Buffalo power play when Thomas Vanek slipped a diagonal pass that Pacioretty put in off Hackett at 10:53 of the third period.
Briere picked the puck out of a crowd and beat Hackett with a wrist shot from close range on a power play at 16:54.
"What I liked was that we didn't change anything when it was 0-0," Therrien said. "We stuck to the game plan and we were rewarded. Hackett played really well for them, but we were patient and disciplined with the puck.
"I expected a tough start after the wins in Toronto and Boston."
The Canadiens had a four-minute power play in the second period when D'Agostini was called for holding and got an extra two for banging his stick on the glass in protest, but failed to cash in.
Sabres defenseman Tyler Myers left the game at 6:15 of the third when he looked to hurt an arm or his ribs crashing into a goalpost. There was no immediate word on his condition.
Myers was in his first game since sitting out five with an arm injury.
With Weise and Moen both injured Monday in Boston, Eller and White returned to the Montreal lineup. Jarred Tinordi replaced veteran Francis Bouillon. ... Ville Leino, who is without a goal in 51 games this season, was back for the Sabres after sitting out two games in place of injured Zenon Konopka. ... The Canadiens swept their four-game season series with Buffalo.