Lenhart missed another good chance minutes later as he latched onto Jean-Baptiste Pierazzi's cross from the left, but this time he headed his effort over the bar.
The home side nearly paid for these missed opportunities when Marcelo Sarvas found space on the edge of the box, although fortunately for San Jose he blasted his shot over the bar.
After the break, San Jose started strongly again and Cordell Cato came within inches of handing them the lead as he burst down the right, but his shot went just over the upright.
The Galaxy could have doubled their advantage through Stefan Ishizaki when he raided down the right and cut back onto his left foot and saw his shot clatter off the post. Kofi Opare tried to knock the rebound into the net but was denied by Busch.
San Jose pressed late in the game to get an equaliser and Lenhart came so close to finally getting his goal only to be denied by a great save from Jaime Penedo, who tipped his header over the bar to earn his side the victory.