Cam Weaver had given the Dynamo a 1-0 advantage in the 61st minute with a goal off an assist from Brad Davis, marking his first tally in more than two years.
But Magee quickly responded, sneaking past the defense to tip in Patrick Nyarko's cross at the goal line for Chicago (7-9-4), which remains five points out of an Eastern Conference playoff berth.
Houston moved to 8-6-6 but fell into sixth place in the West following New England's victory over D.C. United earlier Saturday.
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