Oduro set up the Crew's first goal in the 6th minute when he drew a foul and the ball came to Argentine central midfielder Matias Sanchez, whose shot bounced off defender Jeb Brovsky and into the net.
Oduro doubled the advantage in the 22nd minute, stealing the ball from Montreal's Collen Warner, streaking toward the net and poking it past goalkeeper Troy Perkins for his seventh tally of the season.
The Crew (5-5-5) snapped a three-game winless streak.
The Impact (8-3-2) retained first place in the Eastern Conference despite the loss.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys