By averting their first three-game losing streak since last July, the Red Bulls -- in third place in the Eastern Conference -- improved to 11-9-3 for the season.
Angel’s 14th goal of the season came after an assist by mid-fielder Dane Richards.
It led to the second loss in three games for the Fire (7-10-5), who are in sixth place in the East, just ahead of expansion Toronto FC.
Chicago is in danger of missing the post-season.
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