Rookie goalkeeper Paolo Tornaghi collected his first shutout of the season, stopping four shots in the Fire's home opener.
Oduro scored with a well-placed header in the 28th minute. Midfielder Marco Pappa beat Philadelphia defender Chris Albright with a fake before feeding Oduro, who was about eight yards away when he sent a curling header past goalkeeper Zac MacMath low to his left side.
Philadelphia has lost its first three matches and scored only two goals. Gabriel Gomez had a pair of promising free kicks in the second half Saturday night, but Tornaghi was there each time.
The Fire (1-0-1) forced MacMath to make five saves.
(Copyright 2011 Philadelphia Union. Reprinted by permission)