The Fire grabbed a 2-1 lead on Mike Magee's second goal of the second half, but the Chicago star later missed a chance for a hat trick when he couldn't convert a penalty kick in the 79th minute.
That left the door open for Tissot, who headed in a deflected clearing pass as the Impact (13-9-7) retained third place in the Eastern Conference with 46 points.
Marco Di Vaio netted his MLS-leading 19th goal for Montreal.
The Fire (11-12-7) missed a chance to gain three important points, instead remaining two points out of the playoff picture in the East.
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