Harden missed 14-of-17 shots from the field but made key free throws at the end to finish with 20 points to go with 11 assists.
Parsons put in a game-high 26 points, including 18 on 3-pointers.
The Rockets shot just 37 percent from the field but came away with their third win in four games.
The Warriors got 24 points from Stephen Curry and 22 from Klay Thompson.
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