The visitors took the lead in the third minute when Mike Magee lifted a long ball over the top of the Revolution defence and Quincy Amarikwa powered through a challenge before firing an effort into the top corner.
Chicago continued to press in the early stages and were only denied a second goal by a good save from Bobby Shuttleworth, who tipped Harrison Shipp's low shot past the post.
The resulting corner was only cleared as far as Lovel Palmer, who cracked a shot on the volley that sailed through a crowd of players but went just inches over the bar.
The home side nearly found a leveller when Diego Fagundez fired a ball across the face of goal, but Daigo Kobayashi just couldn't get enough contact at the back post to find the net.
After the break, New England began to up the ante and Sean Johnson was forced into two good saves. First the keeper managed to beat away Chris Tierney's powerful free kick and then tipped Teal Bunbury's low shot past the post.
The Fire were presented with an excellent chance to double their lead when AJ Soares slipped and Matthew Fondy was allowed a free run on goal, but he could only fire his shot tamely at Shuttleworth.
Fondy's miss nearly cost his side when Gonzalo Segares brought down Jerry Bengston in the area and a penalty was awarded. However, Johnson made a great stop to deny Tierney from the spot to secure the three points for his side.