The Galaxy took the lead on 27 minutes when defender Omar Gonzalez headed home to give the visitors something to show for their first-half dominance.
Robbie Keane missed a great chance to double the lead when Galaxy were awarded a penalty on 37 minutes.
The Irishman was unable to keep his effort down, and the former Premier League forward has now missed three of his last four spot kicks in MLS action.
The home side were level after the break when Wondolowski netted his 13th goal of the season.
The striker escaped the attentions of Robbie Rogers to guide home a cross on 65 minutes.