Starting goalie Donovan Ricketts made several early saves before leaving with an arm injury. He was replaced by Josh Saunders in the 23rd minute, but Saunders was sent off for hitting San Jose's Steven Lenhart in the face with an elbow 20 minutes later.
That left the Galaxy (9-2-8) to call on Magee to man the net the rest of the way.
They were lucky, however, because San Jose (5-5-5) didn't get off a decent shot at him until late in the game when Magee had to keep out a close-range shot from Lenhart with his legs.
Simon Dawkins struck the post in the opening 30 seconds for San Jose.