Lee netted 20 points, Dragic added 18 with seven assists and Luis Scola finished with 13 points for the Rockets, who were chasing Utah for the eighth and final playoff spot in the Western Conference.
Houston put the contest away when Brandon Rush connected on a pair of baskets on either side of a Lee 3-pointer, making it 96-92 with 2:23 left in the fourth quarter.
Golden State, meanwhile, fell for the eighth straight time despite Klay Thompson's 24 points.
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