The Sabres could not convert a power play in overtime, but Afinogenov skated down the right side and around rookie defenseman David Hale in the final minute before Brodeur handled his short backhander.
It was one of the better games of the season for Afinogenov, who had one goal in his first 10 games and was benched for five contests last month.
A crowd of 11,146 attended the first regular-season major league sports event in Rochester since an NBA game between the Syracuse Nationals and Philadelphia Warriors in 1960.
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