Seattle (11-3-2) won its third straight and extended its undefeated streak to five games.
Gonzalo Pineda lofted a cross and Barrett headed the feed from the penalty spot to inside the upper left corner of the goal past goalkeeper Bill Hamid. The goal was Barrett's third goal in four games and his fourth of the season.
United (7-5-4) held a significant possession advantage but couldn't find the net. In the 82nd minute, Eddie Johnson narrowly missed tying the game when his header fell wide.
Both teams played without their top scorers – Seattle's Clint Dempsey is playing for the U.S. in the World Cup, and United's Fabian Espindola is serving a suspension.
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