San Antonio opened a 17-point lead late in the contest and survived a Houston surge to win its fourth straight and improve its home record to 12-2.
Parker scored 31 points to go with 10 assists and five rebounds. Tim Duncan produced 30 points and Manu Ginobili added 23 for the Spurs, who shot 57 percent from the floor and made 22-of-24 from the foul line.
The Rockets had a five-game winning streak snapped despite making 52 percent of their shots.
Duncan moved into eighth place on the NBA's all-time shot blocking list. He had two blocks in the game and has 2,544 for his career.