After Kei Kamara gave Kansas City a 1-0 lead with a goal in the 8th minute, Arrieta responded with an equalizer 9 minutes later after taking a pass from Josh Williams and launching a shot past goalkeeper Jimmy Nielsen.
Arrieta then put Columbus (8-7-4) ahead in the 34th minute on a long-distance volley after controlling a back-pass from Graham Zusi.
The win was the second straight for the Crew, while Kansas City (11-7-4) logged its fourth straight home game without a win.
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