Memphis forced 23 turnovers and never trailed while winning for the fifth time in seven games.
Gay scored 28 points and Randolph had 11 rebounds to go with his 26 points. They teamed to make 18-of-32 shots from the field and produced 29 of their points in the second half.
Memphis took an 11-point lead into the fourth quarter and the advantage dropped no lower than seven during the final period.
Paul Millsap, who missed Utah's meeting with Atlanta Wednesday due to a bruised hip, returned to lead the Jazz with 20 points.