The Galaxy had the first attempt of the game as the ball bounced kindly for Robbie Keane outside the box, but his audacious volley went just over the bar.
Seattle brought themselves level in the tie and took the lead on the night when Clint Dempsey and Obafemi Martins linked up inside the box. Martins was brought down and appealed for a penalty, but Dempsey kept going and his low shot found Brad Evans, who tapped home from close range.
Martins should have doubled his side's lead when Dempsey threaded a through-ball into his path but, with only Jaime Penedo to beat, he fired his effort well over the bar.
The Sounders did get their second goal in the 32nd minute as Dempsey found DeAndre Yedlin, who crossed into the area. The Galaxy could only clear the danger as far as Dempsey, who fired a shot past Penedo at his near post.
Los Angeles almost got back into the game immediately when Keane fired at goal from distance, but Stefan Frei made an excellent save to turn the ball past the post.
In the second half, the Galaxy secured the precious away goal when Landon Donovan's corner was cleared into the path of Juninho outside the box, and his effort on the half-volley hit the inside of the post on its way into the back of the net.
Donovan had the chance to put his side in complete control of the game when he latched onto a poor free kick from Osvaldo Alonso and raced through on goal, but his low effort was well saved by Frei.
The Sounders keeper made another outstanding stop to deny the Galaxy minutes later as Donovan crossed into the box for Stefan Ishizaki, but Frei made a fingertip save to tip his header past the post.
Seattle almost went ahead in the tie once more when Gonzalo Pineda lifted a cross into the box and Donovan unintentionally flicked the ball towards goal, but his header went just over his own crossbar.
The home side came within inches of taking the advantage late in the game when a loose ball fell to Dempsey in the box, but he lost his composure at the crucial moment and put his effort off target.
The missed opportunity allowed the Galaxy to see out the win and book a place in the MLS Cup final, where they will take on the New England Revolution.