Beckham scored on a pair of his trademark curling, long-range strikes in the 19th and 24th minutes, and Keane added goals in the 28th and 64th for the Galaxy.
Landon Donovan also scored and supplied an assist as Los Angeles (8-10-2) won its second straight and moved within four points of fourth place in the Western Conference standings behind Vancouver.
Kris Boyd netted two goals and Kosuke Kimura added a tally for the Timbers (5-9-4).
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