German guard Dennis Schroder scored 17 of his 27 points in the first quarter then went quiet until the final period when he drained a brace of three-pointers in a 17-1 scoring run that finally put the Hawks ahead for good.
Schroder added nine assists and six rebounds to offset eight turnovers as the Hawks, battling Milwaukee for fifth place in the Eastern Conference, won for the first time since March 11.
Ersan Ilyasova put up a double-double of 18 points and 12 rebounds for the Hawks. Taurean Price scored 15 and Dwight Howard had 15 points and 11 rebounds.
TJ Warren led the Suns with 24 points and eight rebounds.
Both teams were without key players. Atlanta were missing top scorer Paul Millsap, who missed his sixth game left knee trouble. Kent Bazemore missed his fifth game with a right knee contusion and Thabo Sefolosha missed his second straight game with a right groin strain.
Phoenix were without guard Devin Booker, who scored 70 points in a loss to the Boston Celtics on Friday.
Suns coach Earl Watson said before the game that Booker was nursing an ankle injury.
"We're about 70 points short-handed," Watson quipped.