In the fourth round, Roy faked to the backhand before lifting a shot off the right post and past Tuukka Rask. Benoit Pouliot had the final chance for Boston, but Ryan Miller made the glove save on the wrist shot for the win.
Andrej Sekera scored the lone goal of regulation while Miller stopped 35 shots for the Sabres, who have run off three straight wins.
Zdeno Chara lit the lamp for the Bruins, who have lost three of four. Rask stopped 26 shots in the loss.
Boston has not had consecutive wins since the January 10 and 12, going 8-9-2 during that time.