Ovechkin has failed to score in just two of Washington's 10 games this season and he leads the NHL in goals.
He opened the scoring Thursday with 1:47 to go in the first period and Joel Ward produced the only second-period goal to boost the Capitals' lead.
Braden Holtby was closing in on a shutout before Justin Schultz scored for the Oilers with 2:04 remaining.
Holtby made 30 saves while pushing Washington to its third straight victory. Edmonton's Devan Dubnyk stopped 22-of-26 shots.
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