Thomas Vanek scored the go-ahead goal late in 1 victory over the Canadiens.
Miller made 40 saves, including 11 in the third, as Buffalo killed off all five of Montreal's power-play chances to improve to 4-1-0 on the young season. Jordan Leopold also scored for the Sabres, while Christian Ehrhoff added an empty-netter in the final minute.
Carey Price made 20 saves in defeat, the club's third straight at Bell Centre.
The Canadiens failed to score in the opening period despite outshooting the Sabres, 14-3, but broke the scoreless tie just 2:08 after intermission via Raphael Diaz's first career goal.
Andrei Kostitsyn brought the puck into the offensive zone and left it at the blue line for Max Pacioretty. A trailing Diaz received Pacioretty's feed at the top of the right circle, held the puck long enough to get Miller out of position and wristed his first career goal into the top shelf.
Momentum shifted 10 minutes later when Drew Stafford sent a weak backhander on net from the left circle that hit off Price's chest and bounced out front. Leopold's snap shot from between the circles hit the back of the net at 12:11.
A late icing call left enough time for Buffalo to net the go-ahead goal later in the period. After winning the faceoff, quick tic-tac-toe passing ended with Vanek briefly hesitating from the left circle before beating Price up high with only 2.8 seconds showing.
Montreal pressured Miller throughout the third, only to come up empty-handed. Ehrhoff's full-length empty-netter with under 30 seconds to go sealed the win.
Montreal Alouettes quarterback Anthony Calvillo, who set the CFL career passing yards record last week, was honored before the game...Montreal and the Sabres split six meetings in 2010-11...Derek Roy recorded two assists for Buffalo, which did not score on its only power-play opportunity.