The Galaxy appeared on the way to a second straight win to begin the season when Jack McBean headed a deflection off Mike Magee past Chivas goalkeeper Dan Kennedy to break a scoreless tie in the 83rd minute.
But only 6 minutes later the Goats (1-1-1) earned a point when Alvarez tapped in a cross from Carlos Borja.
Chivas played tough despite a controversial red card given to center back Joaquin Velaquez in the first half, improving to just 4-16-6 all-time against its crosstown rival.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys