The Impact's Marco di Vaio had broken a scoreless tie in the 68th on a forceful volley on the rebound of Sanna Nyassi's shot attempt on the edge of the box.
The Crew (3-1-2) quickly responded when Oduro dribbled to the right of the net and scored with a left-footed shot into the top right corner, netting his third tally of the year.
An apparent earlier goal by Di Vaio was waved off due to an offside call against Montreal (4-2-0), which retains the top spot in the Eastern Conference despite the loss.
The contest was originally scheduled to be played Saturday but was postponed a day because of heavy snow in Montreal.
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