Trailing 3-1 after 41 minutes, the Earthquake rallied for two goals within 3 minutes on either side of halftime.
Victor Bernardez began the comeback with a goal in the 44th minute, beating LA goalkeeper Josh Saunders with a shot to the far side off a Marvin Chavez corner kick.
The Quakes tied it 3 minutes later when Sam Cronin beat Saunders to a long pass from Steven Beitashour and used a sliding touch from 15 yards out for the goal.
Wondolowski then netted his league-leading 14th goal on a back-heeled redirect of a Ramiro Corrales touch in the 61st minute for Western Conference-leading San Jose (11-3-3).
Steven Lenhart also scored for the Earthquake, while San Jose's Jason Hernandez scored an own-goal.
David Beckham and Landon Donovan tallied for the Galaxy (6-9-2), who saw their three-game winning streak snapped.