Randolph also hauled down 13 rebounds.
Darrell Arthur added 14 points, and Mike Conley ended with 11 points and 11 assists for Memphis, which came into the contest leading Houston by 1 1/2 games for the eighth and final Western Conference playoff spot.
Utah, meanwhile, lost its fourth straight road game and fell for the fourth time in six games overall, dropping further out of the West's playoff picture.
Paul Millsap led the Jazz 15 points.
Swim Week Miami Beach 2014 [PHOTOS]