Jonathan Toews netted what turned out to be the game-winner in the second period as Chicago snapped a three-game winless streak.
Antti Raanta turned aside 18-of-20 shots to notch the victory.
The Oilers were led by Ales Hemsky, who provided a goal and an assist.
Boyd Gordon and Taylor each scored and Devan Dubnyk yielded five goals on 41 shots for Edmonton.
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