Harden also provided eight rebounds and five assists for the Rockets, who blew a 25-point lead but eventually emerged with a third win in four games.
The game included a pair of lengthy delays as water dripped from the ceiling of the Verizon Center onto the floor near the scorer's table following a day of heavy rain in Washington.
The contest took more than 3 hours to complete.
Jeremy Lin helped out with 18 points and eight assists.
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