Ivorian Drogba, 37, who joined Montreal in July after a glittering European club career, mainly with Chelsea, headed the Impact in front in the 39th minute after wrestling Chicago defender Jeff Larentowicz to the turf.
Ghanaian midfielder David Accam pulled bottom-placed Chicago level in the 50th minute, before later missing a gilt-edged chance with the goal beckoning.
The Fire paid for the miss and slumped to their fourth straight loss, and first since coach Frank Yallop was fired on Sunday, when Argentine midfielder Andres Romero scored the winner for Montreal in the 76th minute.
The win lifted Montreal, sixth in the Eastern Conference, to 39 points from 28 matches, four points clear of seventh-placed Orlando in the race for the final playoff spot. The Impact have two games in hand.
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In the West, Kansas City remained fifth, missing a chance to climb within one point of first-placed Vancouver.
American striker Will Bruin scored the only goal for Houston in the 67th minute.
Houston defender Oscar Garcia was sent off three minutes later for a second yellow card, but the 10-man Dynamo hung on.
Kansas City have 44 points from 29 games, four points clear of seventh-placed San Jose.
The top six teams in each conference after the 34-game regular season qualify for the playoffs.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Greg Stutchbury)
