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.
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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.
Los Angeles goalie David Bingham was also credited with two saves. Bingham's biggest save was in the 34th minute when he dove to his left to deflect a shot by San Jose's Jackson Yueill out of bounds.
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.
San Jose's Andres Rios took a pass from Marcos Lopez and put a shot over Bingham and into the net in the 89th minute, but the play was ruled offside.
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.
San Jose's Nick Lima received a yellow card in the third minute, while the Galaxy's Daniel Steres and Julian Araujo were booked in the 17th minute and in second-half stoppage time, respectively.
Los Angeles held an 11-7 advantage in shots, but both teams only managed two on goal.
San Jose Earthquakes hold off LA Galaxy in scoreless draw
LA Galaxy manage only two shots on target in a scoreless draw with San Jose. Watch MLS on ESPN+.