A brace from former English Premier League star Robbie Keane proved the difference against the Costa Ricans at the StubHub Center on Tuesday.
Keane, who scored a hat-trick in the MLS on the weekend, struck first on 66 minutes after strong lead-up play from USA international Landon Donovan.
The Ireland international captain wrapped things up with his second in stoppage time from another Donovan assist as the Galaxy moved top of Group Eight in the CCL.
Fellow MLS club Houston Dynamo were unable to register a win of their own though, in a tough road trip to Port of Spain against W Connection.
In a hard-fought clash played in stifling heat, the Dynamo failed to breach the well-organised home defence and had to settle for a 0-0 draw in their opening fixture of the CCL Group Stage.
In the other match on Tuesday, Tijuana of Mexico won 3-2 away to Honduras' Victoria.
