The Rockets won their third in a row and opened a 3 1/2-game cushion over Utah in their bid to capture a playoff berth.
Parsons, who is averaging 15 points a game in his second season in the NBA and whose high game for the year has been 32 points, produced 29 while hitting 12-of-18 from the field.
Houston pulled off the victory despite turning the ball over 19 times and committing eight more fouls than did the Kings.
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