Randolph had 21 points and 11 rebounds and Gasol went for 20 and 10 for the Grizzlies, who have won six of their last seven games and hold the No. 8 seed in the Western Conference.
Memphis, which has won eight in a row at home and six of seven against the Jazz, got 18 points from Mike Conley.
Gordon Hayward, Trey Burke and Alec Burks each scored 16 for the Jazz, who have lost six in a row and 11 of their last 12.
The Jazz, after trailing by as many as 18 in the second quarter, tied the score at 84-84 on Burks' layup in the fourth. But they only scored one more time in the last 5:38 -- on an Enes Kanter dunk.
"We lacked focus coming out of halftime and they were very aggressive," said Memphis coach Dave Joerger. "We made a little change in our coverages and did a good job of getting up on shooters."