Rodríguez's go-ahead score came in the 47th minute for LAFC (9-3-2) and was the only goal in the second half.
Jeremy Ebobisse scored two goals for the Earthquakes (3-6-5) — in the 16th and 31st minutes — to tie the score at 2.
LAFC outshot the Earthquakes 13-7, with a 9-3 edge in shots on goal.
Maxime Crépeau saved just one of the three shots he faced for LAFC. JT Marcinkowski had six saves for San Jose.
This story originally appeared in Los Angeles Times.