A gritty performance from Chivas USA earned the team a deserved point after going down to 10 men late in the first half.
Jack McBean appeared to have won it for the Galaxy with only minutes remaining, but Carlos Alvarez grabbed a late equalizer to stun the defending champions.
The Galaxy took most of the initiative in the first half, attacking the three-man backline of Chivas USA with varying success. Jose Villarreal came closest to opening the scoring when he headed against the crossbar off Omar Gonzalez's headed pass.
The game changed just five minutes from halftime when Ricardo Salazar decided to show Joaquin Velázquez a straight red card after a sliding collision with a Galaxy player, when it appeared either player could have been whistled for a foul.
The strange decision prompted the Galaxy to go further on the attack, and Mike Magee almost opened the scoring when he hit the post five minutes into the second half.
Chivas defended valiantly but finally capitulated just seven minutes from time. A deflected Mike Magee cross popped up in the air, and Jack McBean was on hand to turn a twisting header that was just out of the reach of a diving Dan Kennedy, who could only palm the ball into the back of the net.
The goal appeared to consign the Goats to a loss but shockingly, they grabbed a late equalizer when Carlos Borja was sent through the right flank and delivered a pinpoint low cross which rookie Carlos Alvarez turned home for his first MLS goal, earning his side a share of the spoils.