The Galaxy's victory snapped an 11-game winning streak for the Dynamo (8-3-4).
Dunivant's goal, his first this season, came in the 24th minute as he redirected a shot from Mike Magee to score on Houston goalkeeper Pat Onstad.
The win was just the third this season for Los Angeles (3-3-9) and its second in nine games.
Houston's attack didn't get off a shot until the last minute of the opening half when Kei Kamara headed the ball straight at goalkeeper Donovan Ricketts.
In the second half, Kamara had another chance to score when Brad Davis played him into the box. But Ricketts easily caught the poor chip.
The Galaxy mounted another threat in the 66th minute when Eddie Lewis drove a cross into the area for Edson Buddle, whose header skipped past the post.
Ricketts made his biggest save when he stopped Cam Weaver's shot from close range.
Copyright 2009 by United Press International.
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