Galaxy defender David Junior Lopes was handed a red card and sent off for handling the ball and denying a clear goal on Correa's shot in the 72nd minute.
Correa's first penalty kick went in but the goal but was disallowed when teammate Alejandro Moreno encroached before the shot. Correa scored on Brian Perk in his next try.
Chivas (4-6-1) notched its first home win of the season.
Defending MLS champ Los Angeles (3-6-2) extended its winless streak to five games.