It was the first game of the season for the Senators, who gave the Sabres their second loss in as many outings.
Miller had a tremendous effort in defeat, stopping 45 shots.
Anderson made 35 saves and opened his campaign with a shutout after having recorded three of them during the lockout-shortened 2012-13 season. His career high for shutouts in a season has been seven, established four years ago while with Colorado.
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