Keane came close himself 10 minutes before the break, latching on to Landon Donovan's pass before fizzing an effort narrowly wide of the post.
The Republic of Ireland striker wouldn't have to wait much longer for a goal, however, opening the scoring two minutes later when he slotted a rebound home after Dan Gargan's header caught Dan Kennedy off guard.
It was 2-0 shortly afterwards as the Galaxy completed a two-goal salvo in six minutes at the end of the first half when Stefan Ishizaki produced a sublime chip over the keeper to double his side's lead.
Keane almost had a second for the night soon after the restart when he beat the keeper with an effort, but Carlos Bocanegra was on hand to clear the ball off the line.
It was 3-0 in the 56th minute, however, as Keane and Donovan combined to set up Baggio Husidic for a goal that sealed the points for Los Angeles.
Chivas finally made Brian Perk work for the first time in the 81st minute, but the Galaxy keeper made a comfortable save to ensure a clean sheet to go along with the victory.