Kyle Korver added 14 for the Eastern Conference leaders, who had six players in double figures.
Markieff Morris scored 22, Eric Bledsoe 21 and Marcus Morris 18 for the Suns, who led by as many as 11 points in the third quarter and were up 73-65 entering the fourth.
Atlanta improved to 1-1 on its six-game road trip through the West.
Millsap and Korver each sank two 3s and Kent Bazemore one in the Hawks' late surge, when they went 5 for 6. Atlanta outscored Phoenix 31-14 in the fourth quarter.
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