Espindola collected a pass over the Sounders' back line from Luis Gil and fired in a left-footed volley from 16 yards away, giving RSL (8-3-2) the only offense it would need.
Salt Lake extend its unbeaten streak to five matches with the help of a tough defense that held Seattle striker Fredy Montero without a clear scoring chance during the game.
Seattle (7-2-1) lost for the first time since March 31.
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