The Bruins pulled their own goaltender with 1:06 to go in a desperate attempt to gain the equalizer but Miller stood firm, stopping a Mark Recchi try from the right side with 2 seconds remaining to preserve Buffalo's victory.
Tyler Myers, Paul Gaustad and Tim Kennedy scored for the Sabres, helping lift them to their sixth win in seven games and moving them to within a point of idle Pittsburgh in the battle for the second seed in the Eastern Conference playoff race.
The Bruins got goals from David Krejci and Dennis Seidenberg in the loss.
Goalie Tim Thomas was pulled after letting in three goals on 14 shots in 26-plus minutes and was replaced by Tuukka Rask, who stopped all 19 shots he faced and notched an assist on Seidenberg's tally.
Celebrity Families of 2014 [PHOTOS]