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The Sounders advanced to Monday's Western Conference final against the winner of Thursday's matchup between Sporting Kansas City and Minnesota United.
That winner will claim a berth in the December 12 MLS Cup final against Sunday's Eastern Conference final winner -- either the New England Revolution or Columbus Crew.
After a scoreless first half, the Sounders struck quickly in the second off a corner kick by Uruguayan midfielder Nicolas Lodeiro.
The ball dropped into the heart of the penalty area and O'Neill, a 27-year-old Irishman, leaped high to deflect the ball inside the far post and give Seattle the lead.
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It was O'Neill's first MLS goal since 2014 and first playoff marker.
The Sounders, seeking a third title and fourth trip to the final in five seasons, silenced Dallas from there to complete the 10th playoff shutout for Seattle goalkeeper Stefan Frei of Switzerland.
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