The visitors started the game well and could have gone ahead when Landon Donovan lifted a cross into the box for Alan Gordon, but he guided his header from close range over the bar.
The Galaxy went close again as Marcelo Sarvas found space 25 yards from goal and drilled an effort goalwards, but his shot was well saved by Dan Kennedy.
Kennedy kept his side level again minutes later, this time to deny Gordon as Donovan lifted a free kick into the box and the keeper tipped the forward's powerful header over the bar.
Los Angeles took the lead just before the break when Gyasi Zardes picked up the ball on the edge of the box and curled an effort past Kennedy into the bottom corner.
In the second half, the visitors doubled their lead in spectacular fashion as Robbie Keane found the net with a sublime chip from the edge of the box after skinning Jhon Kennedy Hurtado to give himself the opportunity.
The Galaxy secured their win as they scored their third goal of the game with a slick passing move inside the Chivas box, which culminated in Donovan finding Zardes, who was left with a tap-in into an empty net.
Matters got worse for the home side in the 75th minute when Erick Torres was shown a straight red card for a poor challenge on Baggio Husidic as they ended the match with 10 men.