The Rockets surprised San Antonio with a 40-point opening quarter, one in which Parsons scored 14 points and the Spurs hit just three of their first 19 shots.
Houston built an 18-point lead, but San Antonio fought back to within three early in the final period.
Harden then scored 11 straight points to help put the game away. After losing just two of their first 12 home games this season, the Spurs have dropped two more on their home court in the last five days.
Harden finished with 28 points, hitting 11-of-16 from the field as part of Houston's 52 percent shooting performance. Parsons and Terrence Jones both had 21 while Dwight Howard contributed 15 points and 20 rebounds.