Led by a Robbie Keane goal in the first half and a pair of Landon Donovan goals in the second, Los Angeles was able to hold off a second-half rally from the Red-and-White.
Substitute Paolo Cardozo knocked in his first goal of the season in the 52nd minute for Chivas.
The series is now even at one win a piece this season.
The Galaxy broke the ice in the 14th minute of play when David Beckham made his way with the ball near the half-circle and threaded a pass to the cutting Keane, who was able to find the back of Dan Kennedy's net.
The Rojiblancos had a number of solid looks in the first half, as they took more shots than the Galaxy. Miller Bolaños was active from the opening whistle and was able to work the ball into the box from the left flank a number of times, taking a shot on-goal in the fifth minute and later setting up Nick LaBrocca for a strike inside the box in the 22nd.
Fellow midfielder Ben Zemanski also attacked the Galaxy net. In the 43rd minute he unleashed a powerful strike from about 25 yards out, but Galaxy goalkeeper Josh Saunders was able to get his hands on the shot and prevented any damage.
After the Galaxy went up by two in the 48th minute on Donovan's first goal of the night - a long through-ball from Keane inside the mid-field line - the Rojiblancos got on the board to cut the lead in half.
Midfielder Ryan Smith, from the right wing, worked the ball from just outside the box, leaving behind in a sequence of moves three Galaxy defenders, before dropping it off to Cardozo on his left, who gathered the assist and served it to the back of the net, as he beat Saunders to his left.
The Goats applied plenty of pressure in their final third in the second half, as they knocked on the door on several plays. In the 60th minute, Cardozo nearly found the equalizer after a scrum broke out near the short area, but Saunders was able to deflect the goal attempt to narrowly preserve the lead.
Throughout the match Chivas USA took a number of dangerous free kicks, none more dangerous than sub Juan Pablo Angel's kick in the 81st minute that sailed just right of the post.
The Galaxy found their third and final goal in the 78th minute, after a corner kick produced a scrum inside the short area, where Donovan recovered the loose ball and tapped it in past Kennedy.
THREE DAYS EARLIER, CHIVAS USA defeated the Portland Timbers, 1-0, before a crowd of 13,827 at The Home Depot Center. Midfielder Miller Bolaños' first goal of the season along with Ryan Smith's third assist for the year was all the offense needed for the Red-and-White to collect three points at home.
With Smith and Bolaños in the starting XI, the Goats were able to wreak havoc on both flanks, especially Smith, who now has all three of his assists this season against Portland.
After receiving a long ball from fellow midfielder Nick LaBrocca on the right wing, Smith worked the ball superbly around the Portland defender and into the box where he crossed it to Bolaños, who knocked it into the top of the net in the 16th minute.
The Goats nearly went up a second goal on several occasions. Sub Jorge Villafaña's center into the box from the left sideline found Juan Pablo Angel for the header, but Portland goalkeeper Troy Perkins was able to stop it.
In the 74th minute, the second goal looked as though it was inches away from landing, as Paolo
Cardozo floated a shot over Perkins' head when he came out of his net to break up a pass to Angel. But the ball bounced just wide left of the far post.
Chivas coach Robin Fraser was very pleased with his team's performance against Portland.
"I thought the first half went very well for us, we started off positive," Fraser said. "We did a good job of managing the tempo of the game. At times we possessed well and when we found moments to be dangerous, if not dangerous, we were pretty close to being dangerous. It was good to see us play with that sort of rhythm. In the second half we definitely weren't as good with the ball and weren't as forward thinking as we were in the first half and as a result we ended up defending a lot more.
"Credit to the group, obviously to go down a man for the number of minutes we did, to deal with the daytime game, the group really hung in there. I'm very proud and happy for the win and the shutout."