The Suns outrebounded the Grizzlies 52-35, with 17 of the rebounds coming on the offensive end.
Phoenix won its fifth straight at home and has captured seven of nine overall. Memphis had a five-game winning streak snapped.
The Suns went on an 11-5 run at the end of the third period to take a six-point advantage, and the lead eventually grew to 12 points in the fourth quarter.
Marc Gasol led Memphis with 21 points, eight rebounds and five assists.
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