The Suns climbed within three points when Markieff Morris made a layup with 1:59 to play, but that was as close as they came down the stretch.
Conley hit 11-of-19 from the field and added seven assists. He scored 17 of his points in the second half and was coming off a 30-point effort in an overtime loss to San Antonio Tuesday.
Zach Randolph chipped in 20 points and 13 rebounds for the Grizzlies, who have won all three of their meetings with Phoenix this season.
The Suns were led by 21 points and eight assists from Goran Dragic.
Celebrity Families of 2014 [PHOTOS]