Marc Savard and P.J. Axelsson scored in regulation for Boston, which avoided its longest losing streak of the season. Derek Roy and Jochen Hecht scored for the Sabres, losers of a season-high three straight.
Ryan Miller stopped 35 shots for Buffalo, including an exceptional diving save with his stick on a shot by Paul Mara late in the second period. But he couldn't get his stick on Sturm's shot in the shootout.
The teams each scored two goals in the opening period and remained tied until overtime despite some good chances on both ends.