And the big man was at it again on Monday night, scoring 22 points, grabbing 10 rebounds and even dishing a season-high seven assists in the Grizzlies' 104-94 victory over the Utah Jazz.
"We go as our leader goes," Memphis guard Tony Allen said. "He carried us today."
But he also had plenty of help from a bench that scored 51 points. Jerryd Bayless scored all 17 of his points in the second half while Mike Miller added 15 and Jon Leuer 11. The Jazz were so worried about Randolph's ability down low that they strayed from the Grizzlies' 3-point shooters.
That proved to be a costly mistake. Memphis shot 11 of 20 (55 percent) from 3-point range, using timely shots to brush back all of Utah's rallies. Bayless, Miller and Leuer were a combined 8 of 10 from long range.
"I'm impressed," Memphis coach Dave Joerger said. "We just kept coming harder for longer stretches of time. We kept the turnovers down, which gives us some shots. We got some offensive rebounds. I think our mistakes are glaring at this point. The reason that they are glaring is because there are fewer and fewer of them."
Memphis (12-15) has won two in the row after losing a season-high five straight. Bayless hit two 3-pointers in a row, one at the end of the third quarter and the other at the beginning of the fourth, to help the Grizzlies push out to an 80-71 lead.
Utah made several runs to keep the game close, but never led after late in the first quarter, when the Grizzlies went on an 11-0 to turn a 21-18 deficit into a 29-21 advantage.
"I thought the effort was there. We're trying," Utah coach Tyrone Corbin said. "We had some lulls in there, but the guys are fighting, and, as a result, we had chances in the ballgame. We just couldn't get over the hump."
The Grizzlies pushed out to a 41-29 lead by midway through the second quarter, but nearly lost it before recovering for a 53-48 halftime lead. Randolph led all scorers with 12 first-half points while Burke had 11 for the Jazz.
James Johnson -- a 6-foot-9 forward who the Grizzlies signed last week from the D-League -- once again received extensive playing time. He started his second straight game and played 33 minutes, contributing nine points, five rebounds, four blocks and a constant stream of energy.
He swatted Hayward's 3-point attempt into the seats just before the end of the first quarter and jammed Jefferson's layup attempt back in his face in the third quarter. Both blocks received huge cheers from the bench.
The Grizzlies need all the energy they can get these days while trying to weather a steady stream of injuries. Tayshaun Prince sat out a third straight game because of a sore left knee.
Randolph's seven assists were one short of a career high.
It proved too much for Utah to overcome. The game signaled the end of a long road trip for the Jazz, which spanned 4,684 miles and five games over eight days.
"Their bench played extremely well, and we just didn't match that energy they had especially in the second half," Jefferson said.
Memphis F Jon Leuer made 1 of 2 3-point attempts, which actually dropped his season mark to 14 of 26 (53.8 percent). Leuer has scored in double figures in eight of his last nine games ... Tony Allen was called a technical foul in the third quarter after shoving Utah's John Lucas III. ... The Grizzlies improved to 6-10 at FedExForum.
Follow David Brandt on Twitter: www.twitter.com/davidbrandtAP