Pajoy started the decisive play when he beat the offside trap in the 59th minute and then headed the rebound of a Joe Thorrington shot past goalkeeper Nick Rimando.
United (1-1-0) rebounded with a victory after opening the season with a 2-0 loss to Houston.
Real Salt Lake (1-1-0) fell following a 2-0 defeat of San Jose to begin the season.
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