In the tightly contested Western Conference, Memphis moved two games up in the race for fifth place on Dallas, which is in a three-way fight for sixth and barely holding on to a spot.
"We're now eighth or ninth, so we've got to fight," said Dallas forward Dirk Nowitzki, who led the Mavericks with 17 points and eight rebounds. "We've got to battle and win some games."
Arenas helped the Grizzlies hold on when the Mavericks rallied in the second half. His timely 3-point shooting turned back several Dallas runs, the long-range shooting adding a dimension the Grizzlies have wanted.
"It's like he's a video game player. It's just automatic," Conley said. "It's fun to watch when he's shooting like that, and we need that."
Added Memphis coach Lionel Hollins: "Gilbert hitting the 3s has been huge. He has brought in a new spirit for our guys, and it is contagious."
Memphis claimed the head-to-head tiebreaker with the Mavs by winning the season series 2-1.
"Looking at the standings should get us even more motivated," Dallas coach Rick Carlisle said. "I'm not a big watcher of the standings, but for anybody that is, it brings to the forefront the urgency of the situation."
The Mavericks weathered an early 20-point Memphis advantage and pulled close midway through the third period.
But the Grizzlies never let Dallas take the lead, although four free throws by Nowitzki down the stretch cut the Memphis lead to 92-89 with 21.5 seconds left.
Randolph hit a pair of free throws 6 seconds later, and Marc Gasol stole an inbounds pass in the closing seconds to preserve the Memphis victory.
"Tough isn't the word," Marion said. "It's just frustrating in all aspects. We dug ourselves a deep hole."
Dallas missed 13 of its 14 shots, finishing 2 of 15 in the first quarter. Randolph's 3-pointer as the horn sounded at the end of the first frame gave Memphis a 29-10 lead, the 10 points matching Dallas' season-low for points in a quarter.
"We came out with a fast tempo, getting baskets and stopping them," Randolph said. "They missed a lot of shots in the beginning. It was just coming out and playing our game, making defensive stops and getting out in transition."
Nowitzki missed all five of his shots and was 1 of 7 in the half.
The Mavericks got untracked in the second, scoring the first eight points as Memphis began struggling from the field. Jason Terry, who had 12 points on the night, connected on a couple of 3-pointers, and Dallas got the advantage under double digits, when Carter's drive with 1:36 left in the half made it 43-34.
Memphis carried a 50-39 lead into halftime as Gay had 14 points.
The Mavericks continued to chip into the lead in the third, starting the quarter outscoring Memphis 23-13, a rally capped by a 3-pointer from Carter. That pulled Dallas within 63-62, but Memphis pushed it back to 72-67 entering the final period.
Memphis got the lead to 10 once in the fourth, and maintained a five- to seven-point advantage through much of the quarter. Dallas shot 57 percent in the frame, but that was offset by a half dozen turnovers.
"The turnovers just killed us," Marion said. "That's how they were able to capitalize, and that's how they got the win.
"They played hard, but if we did what we were supposed to do, we should have won this game. I am not taking anything away from them, but that's a loss on us, not as much as on them."
The Mavericks were without reserve forward Ian Mahinmi, who welcomed a new baby girl earlier Saturday. ... Memphis G Tony Allen missed his second straight game after getting popped in the mouth during Wednesday's game at Dallas, resulting in seven stitches inside his mouth. ... The game drew 18,119, Memphis' fourth sellout of the season. ... Marion has at least nine rebounds in six of his last eight games. ... Dallas shot 46.6 percent for the game, losing for only the fourth time this season when shooting better than 45 percent. ... Memphis beat both teams who played in last season's NBA finals on consecutive nights and never trailed in either game. The Grizzlies defeated the Miami Heat 97-82 on Friday night.