Danny Briere added an insurance marker with Montreal on the power play at 16:54 of the third, while Price stood tall down the stretch to help kill off a late Canadiens penalty and secure his fifth shutout of the season and 24th of his career.
With its third straight victory, Montreal moved into sole possession of second place in the Atlantic Division after entering Tuesday's contest tied with the idle Tampa Bay Lightning at 87 points.
Matt Hackett, making just his second start of the season, stopped 33 shots for the cellar-dwelling Sabres, who have lost two straight and nine of their last 10 games. Buffalo sits last in the NHL with 48 points.
Just after Montreal killed off a hooking minor against Douglas Murray near the midpoint of the third, a 3-on-2 counterattack from the Canadiens saw David Desharnais carry the disc down the middle and into the Buffalo zone before dishing to former Sabre Thomas Vanek near the right point.
Vanek then made his way to the top of the right circle before threading the needle to the low left side for a cutting Pacioretty, who got just enough on the puck to send it fluttering past Hackett for a 1-0 lead at 10:53.
With Montreal on the power play just over six minutes later, Briere picked up a loose pick in the low left circle and found the far top corner with a wicked wrister to make it 2-0 at 16:54.
Montreal's P.K. Subban went off for tripping at 18:59, but the Sabres were unable to solve Price.
Following a scoreless first frame, Montreal had a prime opportunity to strike first after Matt D'Agostini was called for holding at 6:10 and then received an unsportsmanlike conduct minor for barking at an official from the penalty box to give the Canadiens a four-minute power play.
However, Hackett came up with some big saves to keep the Canadiens off the board, and the teams went into the third locked in a scoreless stalemate.