Parker finished with 27 points, 12 rebounds and 12 assists while Neal racked up 29 points, including a 3-pointer in overtime that helped lift the NBA-best Spurs to their 11th win in 13 road games.
Manu Ginobli added 22 points, six assists and five rebounds while Danny Green chipped in with 14 points, six boards and five helpers as San Antonio improved to 17-4 overall.
Tim Duncan provided a double-double of 10 points and 13 rebounds in the victory.
The Rockets, meanwhile, dropped their third straight despite 38 points and seven assists from Jeremy Lin.
Omer Asik (21 points, 10 rebounds) and Chandler Parsons (20, seven) also made big contributions in Houston's loss.