It was Harden's second game back after missing two contests with a sore foot and he reached the 30-point mark for the first time since March 17.
He scored 33 points, grabbed seven rebounds and handed out six assists in what was Houston's fourth straight win. The seventh-place Rockets stayed three games in front of the eighth-place Los Angeles Lakers in the Western Conference playoff race.
Jeremy Lin added 22 points for the Rockets, who limited Portland to 2-of-20 from 3-point range.
LaMarcus Aldridge piled up 32 points and 13 rebounds for the Trail Blazers, who have lost seven in a row to fall out of playoff contention.