Sherjill MacDonald's first MLS goal broke the deadlock and gave Chicago three points.
Chris Rolfe drew and converted a penalty inside the opening five minutes to give Chicago the early lead.
New England answered in the 11th minute through Fernando Cardenas. Saer Sene's ball in from the wing caused some issues in the box and Cardenas pounced to level the score.
MacDonald scored 25 minutes into the match, giving his team the lead for good after heading home Patrick Nyarko's cross.
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