Stoa's game-winner came after Brian Elliott stopped Magnus Paajarvi in the top of the fourth round, enabling the Avalanche to break a 10-game losing streak and avoid mathematical elimination from the post-season.
Matt Duchene and Kevin Porter scored in regulation and Elliott finished with 31 saves for Colorado.
Kurtis Foster scored with 3:50 remaining in regulation time to forge a 2-2 tie for the Oilers.
Jordan Eberle also scored and Nikolai Khabibulin stopped 25-of-27 shots for Edmonton.
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