Oduro, who played for Houston from 2009-11, knotted the score when he found the bottom-left corner of the net for his 12th goal of the season.
The tally tied him for second on the MLS goal-scoring list with Landon Donovan and Thierry Henry, and handed the Fire (7-8-16) a crucial road point as they push for a playoff spot with three games left.
Colin Clark tallied for Houston (10-9-13), which tied Philadelphia for second place in the Eastern Conference with 43 points.
Both teams are one point behind East leader Sporting Kansas City with 44 points.
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