Memphis won its fourth straight game while the Mavericks have dropped five out of six.
Dallas played from behind throughout the contest, but closed within three midway through the final period. Gay and Randolph then teamed to score seven straight points and the Mavericks did not threaten from there.
Gay scored 17 points to go with 13 rebounds. Marc Gasol added 11 points and 11 boards. Memphis shot only 40 percent from the field, but forced 22 turnovers.
Shawn Marion had 14 points and 11 rebounds for the Mavericks.