The Sounders had won their previous six league fixtures at CenturyLink Field but had barely settled before LA hit the front in the eighth minute.
With Marcelo Sarvas and Landon Donovan running the show, the Galaxy added further goals in the 18th and 36th minutes as they built what proved to be an unassailable lead in Seattle.
The victory took LA (30 points, plus-13 goal difference) into the play-off spots in the West's standings, with Bruce Arena's men rising two positions to fourth ahead of FC Dallas (30, plus-three) and Vancouver Whitecaps (28, plus-two).
Seattle (38, plus eight) remain six points clear of Real Salt Lake in the Western Conference.
It took just seven minutes for the Galaxy to open the scoring with Sarvas piercing the Sounders' defence to find Donovan, who cut the ball back for Gyasi Zardes to notch his seventh goal of the season.
LA were swarming all over Seattle and doubled their lead 10 minutes later when Donovan tapped home the rebound after Sounders goalkeeper Stefan Frei only managed to parry Sarvas' blistering drive from the edge of the box.
Sarvas was again involved in the build-up when Stefan Ishizaki made it 3-0 in the 36th minute, teeing up the Swedish midfielder on the right-hand side of the penalty area for a flashing first-time shot.
With Seattle looking at just their third loss in nine MLS matches, the hosts started to show some anger in the closing stages of the first half with the Sounders' DeAndre Yedlin and Clint Dempsey clashing with the Galaxy's AJ DeLaGarza and Omar Gonzalez.
Sigi Schmid's home side had the better of the second half but failed to test LA goalkeeper Jaime Penedo on too many occasions, while the feistiness of the first half remained with a number of crunching tackles.
The Galaxy held on, however, claiming their fourth league win in six games.
