Marc Gasol added 15 points and a game-high six assists for the Grizzlies, who won their fourth straight and eighth in their past nine games a night after finishing a season-long five-game homestand. The only loss in that stretch was to Dallas last week at home.
Chandler Parsons and Monta Ellis scored 19 apiece to lead the Mavericks, who failed for the third time to get coach Rick Carlisle his 600th career victory.
Nick Calathes had season highs with 13 points and 27 minutes for Memphis with guard Mike Conley sidelined a night after spraining his left wrist in a win over Orlando.
The Mavericks fell behind 54-44 at halftime thanks to 14 first-half turnovers, including a steal in the backcourt and layup by Calathes right after he made two free throws to give the Grizzlies four points in the last 5 seconds of the first quarter.
The Grizzlies didn't trail again after Calathes hit a 3-pointer early in the second quarter. Two minutes later, Jordan Adams scored five straight points to start a 9-0 run that broke a 36-36 tie.
Dallas quickly pulled within seven early in the third, but Randolph repeatedly hit high-arcing jumpers over Tyson Chandler to keep the Mavericks from getting any closer as they fell 3 1/2 games behind the Southwest Division-leading Grizzlies.
Randolph hit seven straight shots in the second half and was 10 of 15 from the field while finishing with his 15th double-double in the past 16 games. He's had 10 straight double-doubles since returning from a nine-game absence because of a sore right knee.
Grizzlies: G Tony Allen missed his second straight game a left ankle sprain. ... Vince Carter scored 12 points in his first visit to Dallas since signing with Memphis as a free agent in the offseason. Carter, who spent three seasons with the Mavericks, got a warm ovation when he came off the bench late in the first quarter.
Mavericks: Ellis got a technical foul for arguing after he was called for charging late in the first half. Carter made the free throw to give Memphis its first double-digit lead at 52-42. ... Before Tuesday, Parsons was limited to one rebound in consecutive games for the first time since his rookie year in 2011-12. He had two against the Grizzlies.
Grizzlies: Home against Denver on Thursday.Mavericks: At Houston on Wednesday in second of four games in five nights.