Parsons put in 31 points and grabbed 10 rebounds, and Howard supplied 24 and 12 for the Rockets, who reeled off a fifth win in six games.
James Harden contributed 22 points, six rebounds and five assists. Patrick Beverly added 17 points in his return from a 14-game injury absence (broken hand).
The Trail Blazers had their five-game winning streak snapped despite 27 points and 20 rebounds from LaMarcus Aldridge.
Damian Lillard netted 24 points and Wesley Matthews added 18.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged