The Earthquakes were coming off a 7-1 loss Thursday at Seattle and had a 5-1 defeat to Los Angeles FC the previous week.
San Jose remains winless since returning from the MLS is Back Tournament outside Orlando, Fla.
The Galaxy had their four-match winning streak snapped and missed an opportunity to move into a tie for third place in the Western Conference.
The match marked the return of Galaxy star Javier "Chicharito" Hernandez, Mexico's all-time leading scorer who suffered a calf injury in the tourney in Florida and hadn't played since. Hernandez came on as a substitute in the 57th minute for forward Ethan Zubak, but was unable to help Los Angeles get on the scoreboard.
Vega's biggest save came in the 75th minute, diving to his left to stop a header by Sebastian Lletget after a short Los Angeles corner kick.
Los Angeles held an 11-7 advantage in shots, but both teams only managed two on goal.