Peter Mueller scored the game-winning goal in 4, on Wednesday at First Niagara Center.
Mueller went in with speed and ripped a quick wrist shot just under the glove of Sabres netminder Ryan Miller. Tyler Ennis had a chance to keep the shootout going for the Sabres, but he lost the puck as he went to make a move, sealing the comeback win for the Avs.
Mueller added an assist and Jamie McGinn scored twice, while David Jones and Gabriel Landeskog also lit the lamp for the Avalanche, who moved into seventh place in the Western Conference. Paul Stastny contributed two helpers and Semyon Varlamov made 20 saves in the victory.
Marcus Foligno scored twice, Drew Stafford added a goal and two assists, Alexander Sulzer scored and Ennis had three helpers for the Sabres, who are three points back of idle Washington for eighth place in the East.
Miller was tagged for four goals on 42 shots in the loss.