Randolph was especially effective in the second half when he netted 22 of his points, helping the Grizzlies wipe out a 16-point deficit and notch their fifth win in six games.
The Grizzlies improved to 9-1 at home with the victory.
The Suns couldn't avoid a fourth straight loss despite 19 points and seven assists from Goran Dragic.
Luis Scola provided 16 points and eight boards for Phoenix.
Toddler uninjured after being knocked over by Obama family dog
Ron Burgundy interviews Peyton Manning on SportsCenter