A quiet opening period saw Galaxy spurn the only clear-cut opportunity when Christian Wilhelmsson's chipped finish trickled agonisingly wide.
Galaxy began brightly after the break and took the lead when Robbie Keane tapped home from close range.
Less than ten minutes later Galaxy restored their advantage through Edson Buddle when he guided in a cross from Sean Franklin.
LA could only hold onto their lead for five minutes as San Jose fought back for a second time when Chris Wondolowski reacted quickest to finish a precise corner from Chavez.
Both sides pushed for a winning goal but were forced to settle for a point apiece.
The draw confirms that San Jose will lift the Supporters Shield for the best record during the regular season while Galaxy cement their playoff place in the Western Conference.