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.
Swim Week Miami Beach 2014 [PHOTOS]