Houston got 17 points apiece from Aaron Brooks and Luis Scola in its second victory in three games.
Zach Randolph scored 22 points and had seven rebounds for the Grizzlies, who lost their fifth game in their last six outings. Rudy Gay added 20.
The Grizzlies trailed 59-55 at halftime and 88-74 at the end of the third quarter but began the fourth with a 14-2 run that got them back into the game. Memphis pulled to within two points three times, and each time the Rockets put together enough of a surge to give themselves some breathing room.
The final Memphis rally was capped by a pair of Mike Conley free throws that made it 103-101 with 2:26 to play. Houston then scored the next six points to make it 109-101 with 1:10 to play.
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