Miller has 25 shutouts in his nine-year career, all of it spent with the Sabres. His best single-season total has been five, which he has reached in each of the last three years.
Buffalo scored twice in each period with Jason Pominville producing goals in the first and third stanzas to run his season total to 19.
Christian Ehroff opened the scoring 6:23 into the game and Drew Stafford ended it with 1:02 left in the contest.
Tuukka Rask gave up three goals on 10 shots before giving way to Tim Thomas. Buffalo touched Thomas for three goals on 19 shots. It was Boston's third loss in four games, but the Bruins still have a six-point lead over Toronto in the Northeast Division.