The hosts started brightly and Galaxy keeper Carlo Cudicini had to do well to deny Jose Manuel Rivera as his low volley looked destined for the net, but the former Tottenham Hotspur man got down and made the save.
However, Zardes was not to be denied minutes later as he gave his side the lead just before half time when he headed home into the top corner from Landon Donovan's free kick.
After the break, Zardes should have doubled his and the Galaxy's tally but he could only head his effort against the post after Omar Gonzalez had teed him up at the back post.
Zardes yet again could have put the game out of the reach of Chivas but in a one-on-one situation with Kennedy he could only fire the ball straight at the keeper.
Chivas tried to rally late on to get an equaliser but the visitors held firm defensively to win the three points.