Goals by Clarke MacArthur, Jason Pominville and Derek Roy staked Buffalo to a 3-0 lead after the first period, making Miller's task much easier.
His shutout streak ended at 148 minutes and 31 seconds in the third period.
Tim Kennedy, Andrej Sekera and Mike Grier also scored. Thomas Vanek had three assists, with Jochen Hecht and Pominville adding one assist each for the Sabres, who recorded their third four-game winning streak this season.
Montreal got one goal each from Scott Gomez and Josh Gorges.
Net-minder Jaroslav Halak was beaten six times on 31 shots for the Canadiens, who have lost four in a row and five of six.
Copyright 2009 by United Press International.
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