Randolph netted 19 points and grabbed 12 rebounds while Leuer came off the bench to add 16 and 12 as the Grizzlies registered just their third win in eight games.
Mike Conley helped out with 13 points and seven assists.
The Magic lost for a sixth straight time despite 19 points, 11 rebounds and four blocks from Andrew Nicholson.
Jameer Nelson (19 points, five assists) Arron Afflalo (17 points) and Glen Davis (16, nine rebounds) also reached double figures for Orlando.
2014: The Year in Music [PHOTOS]