A day after playing the full 90 minutes for England in a 2-1 friendly defeat by Germany in London, Beckham was on the pitch throughout as the Galaxy slipped to their ninth defeat in 17 MLS games.
Chivas striker Maykel Galindo opened the scoring in the 59th minute, sliding the ball past Galaxy goalkeeper Joe Cannon after pouncing on a defensive blunder by Kyle Veris.
Ten minutes later, defender Francisco Mendoza set up Galindo for his second goal, and 10th of the season, with a pinpoint pass that split the Galaxy defence from the right.
Mendoza made it 3-0 with a perfectly weighted left-footed shot in the 88th minute, with Cannon stranded, to put the gloss on Chivas's 10th win of their MLS campaign.
Despite the return from injury of experienced Portuguese defender Abel Xavier, the Galaxy came under continual pressure from a spirited Chivas attack, especially in the opening half.
Galindo found space in the penalty area in the 10th minute but his right-footed blast was parried away by Galaxy keeper Cannon.
"Right at the end he looked hobbled," he said. "I used him tonight and I shouldn't have done that.
"I don't like to put players like David in jeopardy of getting injured, and that wasn't the intention.
"We wanted to make sure his ankle was okay and he said he was okay to start," Yallop added, referring to the left ankle injury that has hampered Beckham for the last two months.
"You can still tell now that he is sore, he's still not 100 percent."
Despite the return from injury of experienced Portuguese defender Abel Xavier, the Galaxy came under continual pressure from a spirited Chivas attack, especially in the opening half when Cannon was required to make several good saves.
The Galaxy were fortunate not to concede a penalty in the 31st minute when Xavier, tackling back, brought Francisco Mendoza down in the area.
Beckham took his first free kick in the 37th minute but it was dealt with adequately by the Chivas defence.
The opening half ended with a fracas in the middle of the pitch and red cards being issued to Galaxy midfielder Kevin Harmse and Chivas defender Alex Zotinca.
Harmse was head-butted by Zotinca in return for a punch to the stomach, a clash sparked when Beckham squared up to Chivas midfielder Jesse Marsch after being the victim of a mistimed tackle.
The Galaxy, who have won only three of their 17 MLS games this season, remain second bottom in the Western standings.
Chivas, with 10 wins out of 19, stay in third spot, seven points behind the pacesetting Houston Dynamo.