Harden also had seven rebounds and Howard pulled down 13, giving the pair 62 points and 20 boards in the game.
Jeremy Lin and Patrick Beverly added a dozen points apiece from the backcourt to get Houston back on track after losing their first game of the season Monday against the Clippers.
Damian Lillard led Portland with 22 points. LeMarcus Aldridge was right behind with 21.
Portland trailed by as many as 18 points in the third period and cut the Houston lead to 93-88 with 7:41 left in the game. Beverly and Harden then hit consecutive 3-point shots to widen the gap.