The home side created the first opening when Shaun Maloney raided down the left and lifted the ball into the six-yard box for the head of David Accam, but he directed his effort over the bar.
New England went ahead in the 28th minute as Scott Caldwell whipped a cross in from the left, which was cleared into the path of Lee Nguyen who buried his effort into the bottom corner.
Accam tried to respond for the Fire when he raided forward to the edge of the box, but his low drive was saved by Brad Knighton.
Chicago were handed the chance to get back into the game just before the break when Accam was brought down in the box. Maloney took the spot kick and fired his effort past Knighton to level the scores.
In the second half, Razvan Cocis almost handed the home side the lead when he fired an effort from distance, which sailed inches over the crossbar.
Chicago pushed ahead in the 75th minute when a cross caused havoc in the penalty area and Cocis pounced on the loose ball and powered his strike past Knighton.
However, the Revolution got back into the match immediately though Kelyn Rowe as he latched on to Chris Tierney's low cross into the box and slotted the ball into the net.
New England thought they had snatched all three points when Charlie Davies fired an effort past Sean Johnson, but the goal was ruled out for offside, leaving both teams to settle for a point apiece.