With the game in a scoreless deadlock, Robbie Keane fed a pass to substitute Magee, who knocked a left-footed shot from outside the box into the bottom left corner.
Josh Saunders made four saves for the Galaxy, who wrapped up the regular season with a 16-12-6 record and the fourth seed in the Western Conference.
They will face the Vancouver Whitecaps in one-game elimination contest Thursday for the right to meet the San Jose Earthquakes in the first round beginning Sunday.
The Sounders, meanwhile, finished with a 15-8-11 record, good for third in the West. They will face Real Salt Lake in the first round starting Saturday.