Frye scored 20 points and Jared Dudley had 17 for the Suns, who let Atlanta back in the game early in the fourth quarter on a 14-3 run before putting together a surge of their own. Phoenix has won 16 of the last 18 times Atlanta has traveled to Arizona.
Atlanta was led by Josh Smith with 26 points. It was the third straight loss for the Hawks.
Steve Nash had 13 points for Phoenix and moved into 10th place on the NBA's all-time 3-point field goal list with 1,547.
Celebrity Families of 2014 [PHOTOS]