The Sounders conceded a fifth-minute penalty to Erick Torres but rallied thanks to a 24th-minmute effort from Lamar Neagle before Goats midfielder Marco Delgado was sent off with just over 15 minutes remaining.
In the 81st minute, Sounders star Clint Dempsey played a neat one-two with Obafemi Martins allowing the Nigerian ace to slot home past an advancing Dan Kennedy to give the visitors the victory at the StubHub Center.
After the match, Dempsey spoke of the importance of securing early wins in the season while touching on the burgeoning on-field relationship with former Inter Milan and Newcastle United attacker Martins.
"It's always good to win, to move up the table to where we should be. We put in a good performance tonight, another good performance on the road, so we're happy," said Dempsey who also had a hand in Neagle's equalizer.
"We're on a good run. It's about keeping it going and it's about the fact that we're moving up the table. We've got to keep going."
And on the Martins partnership, he added: "There were times we linked up pretty well. I was able to put him through this time.
"He went close on one occasion and scored on the other one. (I'm) happy with him scoring, happy to contribute in the game getting two assists."
The Sounders now sit third on the Western Conference table with four wins and one draw from their opening seven fixtures of the 2014 MLS season.
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