Sensational Miller stones Bruins
Andrej Sekera scored in regulation and Thomas Vanek added a shootout goal for the Sabres, who moved within five points of Florida for eighth place in the Eastern Conference.
The Bruins, who won at St. Louis on Wednesday, have not won back-to-back games since Jan. 10 and 12.
David Krejci went to the backhand on Boston's first attempt in the shootout, skipping it over Miller's pad. Vanek responded with a blast from the slot to knot it at a goal apiece.
After three total missed opportunities, Roy went wide and cut to the slot, beating Tuukka Rask for the clincher in the fourth round.
The Bruins got the tying goal at the 3:36 mark of the third period on the power play. Chara intercepted a clearing attempt and blasted a shot from the right point.
The Sabres had taken the lead with 5:15 left in the second, when Sekera took a feed from Tyler Ennis and beat Rask with a wrister from the right face-off circle.
GAME NOTEBOOK: The Bruins did not commit a penalty in the contest. ... Buffalo captain Jason Pominville was held off the scoresheet for only the second time in the last 10 games. ... The Bruins squandered a power-play opportunity in overtime.