On the play, Oduro broke in on goal after getting a pass from Eddie Gaven and sped past a pair of defenders, launching a sharp-angle volley that found a space between the post and Union goalkeeper Zac MacMath.
The Crew (2-1-2) improved to 7-0-4 in 11 all-time home contests against Philadelphia with the result.
Jack McInerney scored in the 34th minute for the Union (2-2-1).
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