Memphis had dropped games against San Antonio and Oklahoma City before turning in a 56 percent shooting effort against the Rockets. Houston has lost two of its first three.
The Grizzlies led by six at halftime before outscoring Houston by 15 in the third period.
Randolph scored 23 points and had nine rebounds. Gasol pitched in 20 points. Memphis did not make a 3-pointer during the entire game.
Kevin Martin made 7-of-11 shots from the field and led Houston with 21 points.