A Birchall goal early in the second half gave Columbus three points.
After an opening half where neither side could open the scoring, despite Columbus having a goal called back for offside, it took under a minute of the second half for the Crew to take the lead.
Arrieta took a free kick quickly, slotting it between defenders and springing Birchall through the line where he finished calmly.
Minutes late Dwayne De Rosario tapped home a rebound for what looked like the equalizer, but he was also ruled offside.
Despite a strong push for the equalizer and several good chances for United, Andy Gruenebaum and his defense managed to keep the clean sheet for Columbus in the win.
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