Khudobin, taking over in net while the Bruins rested Tuuka Rask, turned aside all eight shots he saw in the final period in backstopping Boston to its eighth win in 10 games to start the season.
Patrice Bergeron scored the go-ahead goal 7:52 into the third period after the Sabres' Mike Weber was penalized for shooting the puck into the crowd.
Brad Marchand also scored and Milan Lucic added an empty-netter for the Northeast Division-leading Bruins.
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