The Mavericks raced out of the gate to lead by 19 after one period and were still in front by 13 at the half.
Dallas then scored only five points in the third quarter, going scoreless for more than 8 minutes to start the half while Memphis was enjoying a 20-point run.
It was the eighth straight Memphis victory and the Mavericks' third consecutive loss.
Randolph had 21 points and 10 rebounds while Gasol produced 20 points and 11 boards. Quincy Pondexter added 12 points off the bench for the Grizzlies, who won despite making only 37 percent of their field goal tries.
Dallas was led by Shawn Marion with 16 points.
Notable deaths of 2014 [PHOTOS]
Spurs hit the road to battle high-flying Suns