Terrence Jones finished with 20 points for Houston, 10 in the fourth quarter when the Rockets pulled away to win their fourth straight.
The Rockets broke open an 83-all game to eventually lead by 18 down the stretch as Memphis managed only eight points after the teams were deadlocked.
The Rockets connected on 18 of 35 from outside the arc compared to only 7 of 18 for Memphis. Houston dominated the boards 42-31, including 18 from the offensive glass. That led to a 28-12 advantage in second-chance points.
Memphis, which trailed by as many as 13 in the first half, opened the second half with a 13-2 rally to erase a 9-point halftime deficit.
The Grizzlies couldn’t maintain the advantage as the Rockets controlled the boards, especially the offensive glass. By the end of the third, Houston was outrebounding Memphis 32-21, including 15 offensive rebounds leading to 23 second-chance points through three quarters.
Carter tied the game at 83 on a 3-point play with 7:35 remaining. But the Memphis offense stalled as Jones and Howard carried the Rockets offense.
Houston used 3-point shooting in the first half to take a 51-44 lead into intermission. Thornton gave the Rockets a boost off the bench, hitting three of four shots, including a pair from outside the arc. Thornton had 11 in the half, while Harden and Ariza scored 10 each.
Howard was already on the verge of his double-double with eight points and eight rebounds.
Gasol and Lee scored 10 each in the half for Memphis. Lee’s included a 3-pointer as the horn sounded to cut the Rockets lead to single digits at the break.
Rockets: Howard recorded his 17th double-double of the season. .Houston had lost the first two games in the season series. .Rockets G Ty Lawson did not play, serving the last game of a three-game suspension by the league. .Howard took only 13 shots in the first two games between the two teams this season. He took 10 Tuesday night and converted all five of his free throws, including four as the Rockets pulled away.
Grizzlies: Memphis played without starting G Mike Conley, who missed his fourth straight game with sore left Achilles, and F Matt Barnes, who sat out his first with a right thumb injury. .Randolph moved past Larry Bird (8,974) into 50th place on the all-time rebounding list in the third quarter.