The Crew got off to the perfect start in the sixth minute when they were awarded a penalty after Sean Johnson brought down Dominic Oduro. Federico Higuain made no mistake in dispatching the spot kick into the bottom corner.
After the break, the Fire did find an equaliser as Joel Lindpere raided down the left and lifted a cross to the back post where Duka was unmarked and was left with a simple finish.
Minutes later Chicago took the lead when Lindpere did well again as he hit a pinpoint cross into the penalty area and Mike Magee latched onto the ball and headed it past Gruenebaum.
Higuain almost got the Crew back into the game as he dribbled through several of the visitors' defenders before firing a low shot at goal, which Johnson did well to beat away.
Columbus continued to push and went close again but Bernardo Anor's right-footed volley went just the wrong side of the post as Chicago held out for the win.