Zardes scored off a free kick from Landon Donovan in the 44th minute. It was his second goal this season.
Donovan's assist tied him with Preki for the third-most in MLS history with 112. The 31-year-old player is now two assists behind Carlos Valderrama for second place and 23 behind all-time leader Steve Ralston.
The victory for Los Angeles (7-6-5) was its first in four games. Chivas (3-10-2) hasn't recorded a win since March 30.