Marcelo Sarvas scored the only goal of the game on 52 minutes as Galaxy drew first blood and moved within 90 minutes of a second MLS Cup final in two years.
It was Seattle who were beaten by their California counterparts in this regional final in 2012, but there were no signs that they would avenge that defeat early on as Galaxy dominated and fashioned three good chances inside seven minutes.
First, Robbie Keane, who has scored 19 times this season, missed two glorious opportunities to break the 20-goal barrier, while Gyasi Zardes forced Stefan Frei into a fine fingertip save at his near post.
With 34 goals, no team scored more than the Sounders away from home during the regular season, but Sigi Schmid's side struggled to take that free-scoring form into the StubHub Center.
However, they could, and perhaps should, have moved ahead early in the second half as Penedo denied the ex-Premier League duo again. Martins's clever backheel released Dempsey, but the Galaxy stopper stood up well to palm away the American's dinked effort.
It proved a key moment as Bruce Arena's side broke the deadlock minutes later when Sarvas took aim from just outside the box and watched his deflected effort wrong-foot Frei to open the scoring.
Galaxy very nearly placed one foot in the MLS Cup final, with Stefan Ishizaki crashing a superb free kick against the bar, before volleying Keane's cross high and wide from close range on 72 minutes.