The score was tied 5-5 in the 10th when Hamilton came to the plate with one out and pounded a pitch from Josh Fields (1-3) into the right field bleachers for his 18th homer of the year.
The blow made a winner of Ernesto Frieri (1-4), who had hurled two innings of scoreless relief for Los Angeles.
Brett Wallace hit a two-run homer and added an RBI single for Houston.
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