The hosts were quickest out of the starting blocks in the early stages, with Erick Torres striking the upright in the sixth minute.
Felix Borja then powered towards the Earthquakes goal several minutes later, but was unable to make the most of the opportunity.
In the 32nd minute, the deadlock was broken by the home side when Torres fired towards goal, and despite the shot failing to go in, Borja pounced on the rebound to prod home.
Wondolowski attempted to draw his side level three minutes after the restart, but his header proved unsuccessful, while Yannick Djalo also threatened the Chivas goal to no avail moments later.
The majority of the second half proved a mixture of crunching challenges from both sides and Earthquakes efforts, but the hosts were able to see the game out and secure all three points.