Harden was fouled on a 3-point attempt and made all three free throws before hitting a 3-pointer for a 6-0 run that pushed Houston's lead to 79-61 early in the third quarter.
The Trail Blazers answered with a 9-0 spurt to cut the lead to 79-70. Aldridge had a 3-point play during that stretch and Lillard capped it with two free throws when he was fouled by Howard, who also got a technical on the play.
The Rockets scored for the first time in almost three minutes on a layup by Parsons with about seven minutes left in the quarter. Nicolas Batum made a layup before Parsons added a 3-pointer to extend Houston's lead to 84-72.
Mo Williams got Portland within seven points when he opened the second quarter with a jump shot. But Houston countered with eight straight points powered by two 3-pointers from Omri Casspi to push the lead to 45-30.
Five straight points by Matthews a couple of minutes later cut Houston's lead to 12 points. The Rockets responded again, scoring seven points in a row to extend the lead to 60-41.
Casspi scored five quick points soon after that to extend Houston's lead to 71-49. Portland scored the last seven points of the half to get within 71-56 at the break.
The Rockets made 10 of 13 3-pointers in the first half to help them to score more than 70 points in a half for the second time in a week.
Houston scored on its first 11 possessions to build a 25-11 lead. Beverley, who returned to the starting lineup after missing 14 games following surgery to repair a broken right hand, had two 3-pointers in that span and Harden had one.
NOTES: Houston's Terrence Jones, who scored a career-high 36 points in the last game, sat out with a deep thigh bruise. Donatas Motiejunas started in his place and finished with nine points and nine rebounds. ... The Trail Blazers have scored at least 98 points in 29 games in a row. ... Batum injured one of his fingers and said he "felt it crack" but wasn't sure of the extent of the injury after the game.