Bourque injected some life into what had been an uneventful first period with Montreal's 10th power-play goal of the season. Andrei Markov’s stretch pass — tipped along the way by Tomas Plekanec — found Brian Gionta along the right boards. Gionta waited before passing it on to Bourque, who drove to the net for his second of the season.
Montreal took a 2-0 lead for the fifth time in its seven games early in the second. Gallagher and fellow rookie Alex Galchenyuk completed a nifty 2-on-1 that Gallagher capped with his third of the season as the puck went in off Sabres defenceman Christian Ehrhoff at 2:03.
Desharnais, who has struggled this season, finally got his first at 10:08. Just seconds after Sabres forward Tyler Ennis hit the crossbar, the diminutive Canadiens centre took a pass from Eller in the high slot and fired a shot past Miller.
Eller added to Buffalo's misery with his first goal of the season just 28 seconds later.
Plekanec set up Bourque's second goal of the game at 1:22 of the third. The Czech centre showed patience on a 2-on-1, waiting out Buffalo defenceman Mike Weber’s attempt to block the pass before easily placing it on Bourque’s stick.
Thomas Vanek broke Price's shutout bid with a short-handed goal at 3:01.
Desharnais picked up his second of the season on the player play at 12:43. Defenceman P.K. Subban, making his season debut after signing a new contract Monday, earned an assist.
NOTES: Defenceman Yannick Weber and forward Ryan White were scratches for the Canadiens, who went with 11 forwards and seven defencemen . . . Buffalo's one shot in the first was its fewest in a regulation period since Oct. 7, 2011 versus Anaheim when the Sabres had none in the third . . . Montreal last allowed one shot in a period Oct. 13, 2011 versus Calgary.