Paul Millsap added 14 points for Atlanta, which led the entire way. Kris Humphries had 13, Malcolm Delaney scored 12 and Thabo Sefolosha finished with 10.
Brook Lopez scored 20 points for the Nets, who have lost seven straight and 12 of 13. Bojan Bogdanovic added 16 and Sean Kilpatrick 14.
Caris LeVert (11 points) and Rondae Hollis-Jefferson (10) also scored in double digits for Brooklyn.
Lopez's 3-pointer brought the Nets to 89-78 with 9:44 left. But the Hawks responded with a 24-8 run and opened their largest lead of the night, 113-86, on Taurean Prince's two free throws with 2:02 remaining.
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