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.
2014: The Year in Fashion [PHOTOS]
UPI Sports Results for September 19, 2014