The Hawks took a 14-point lead into the fourth period and were not threatened the rest of the way, converting 12-of-23 from 3-point range.
Phoenix played the middle game of a three-game road trip covering four days, one that will end Saturday in Washington.
Goran Dragic had 21 points for the Suns.
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards
Charlize Theron not engaged to Sean Penn 'yet'