Landon Donovan scored his 200th career goal to help the Galaxy maintain control of the SuperClasico after the Goats won earlier in the season.
Keane opened the scoring in the 14th minute, beating Chivas defender Danny Califf to a David Beckham through ball to finish past goalkeeper Dan Kennedy.
Keane turned provider two minutes after halftime, springing Donovan past the Chivas offside trap for another solo finish to make it 2-0 Galaxy.
But Chivas fought back. Midfielder Ryan Smith cut in from the right wing, drawing three Galaxy defenders before laying off for former Galaxy man Paolo Cardozo, who beat Josh Saunders at the near post to score his first MLS goal against his old club in the 52nd minute.
The goal opened the game up, as Chivas threatened the Galaxy penalty box and Donvan hit the post in the 62nd and 76th minutes.
Donovan scored from point-blank range in the 78th minute following a scramble in the penalty box to cap the scoring.
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