Agudelo provided the go-ahead tally in the 54th minute after streaking past the Fire defenders and chipping the ball over out-of-position goalkeeper Sean Johnson with a right-footed shot.
Kelyn Rowe added an insurance goal in stoppage time for the Revs (9-9-6), who, like Chicago, began the night on the outside of the Eastern Conference playoff picture.
Johnson finished with six saves for the Fire (9-10-4).
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