The Rockets made up for Howard's slow night with four players in double figures. Terrence Jones scored 20 points, and Chandler Parsons had 15 points, 11 rebounds and five assists. Jeremy Lin had 14 of his 18 points in the fourth.
Trailing 76-66 with 10:55 to go, Houston used a 21-5 run over nearly six minutes to take an 87-81 lead on two Harden free throws with five minutes left. Lin powered the surge with 10 points, including two 3-pointers, and Harden added six points in the decisive stretch.
"I just tried to stay aggressive," Lin said. "I know I had a lot of mistakes early on, and I am thankful to God that I got in a rhythm. We really didn't feel good out there. It was an ugly game all around."
After trading 3-pointers, Harden extended Houston's lead to eight on a jumper with 1:49 remaining. Tayshaun Prince hit a 3-pointer to cut the lead to five, but Houston went 8 for 10 at the line to close it out.
The Rockets were just 5 for 24 from beyond the arc against the Grizzlies. But they made three 3s in the fourth quarter and enjoyed a dominant night at the line, making 33 of 40 free throws, compared to 11 for 20 for the Grizzlies.
Memphis reserve James Johnson had 12 points, and Kosta Koufos had five points and 11 boards to help the Grizzlies to a 49-41 rebounding advantage, including a 20-7 margin on the offensive glass that led to 21 second-chance points.
"I don't think it got away anywhere," Memphis coach Dave Joerner said. "They made shots, we didn't score, we had 12 points going into the last minute (of the fourth quarter). I think going on the road, it can be difficult. They're a good team, and they made plays."
NOTES: Houston C Greg Smith missed his third consecutive game with a sprained right knee. ... Prince started after missing the last three games with left knee soreness. He finished with nine points. ... The Rockets re-hired Gersson Rosas to co-lead their scouting and player personnel department with Gianluca Pascucci. Rosas was hired as Dallas general manager in the offseason, but he left the Mavericks a little more than three months after being hired.