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.
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