Ibrahimovic's goals marked his eighth and ninth of season since he made his Galaxy debut on March 31. He's scored twice in four separate games for L.A., which has lost just once in its last six MLS matches and improved its all-time record at Stanford Stadium to 1-4-2.
Meanwhile, Wondolowski's pair of goals pushed him to 140 in his MLS career as San Jose drew a third straight match after losing four straight.
At age 35, Wondolowski is now just five goals away from the MLS career record, held by Landon Donovan. He has six this season, with both of his goals Saturday originating from penalty kicks.
Romain Alessandrini also scored for the Galaxy and Valeri Qazaishvili scored for the Quakes.
Ibrahimovic opened the scoring less than a minute into the match, when he took Chris Pontius' cross and hammered a volley beyond San Jose keeper Andrew Tarbell from the right side of the penalty area.
Wondolowski drew San Jose level after it earned its first penalty of the match. Galaxy keeper David Bingham saved Wondolowski's first attempt, but could not react in time to prevent the forward from driving in his own rebound.
Alessandrini gave Los Angeles the lead again on a well-struck free kick from a tight angle in the 20th minute, and then Ibrahimovic made it 3-1 on another set piece five minutes after that.
About 30 yards from goal and facing a defensive wall, Ibrahimovic drove his shot low so it snuck under leaping San Jose defenders and then between Tarbell and his right post.
Qazaishvili pulled a goal back for San Jose before half-time, and then Wondolowski tied it 24 minutes into the second half on another penalty. Bingham guessed the right direction again, but this time couldn't catch up to the pace of Wondolowski's finish.
San Jose 3-3 LA Galaxy: Wondo, Ibra shine in Clasico - Via MLS
Zlatan Ibrahimovic and Chris Wondolowski both scored twice as the latest California Clasico ended all square in San Jose.