The Hawks kept Cavs star-man LeBron James subdued, limiting him to just 18 points, and were themselves indebted to 19 points, nine rebounds and six assists from Al Horford.
Kyrie Irving, so impressive since returning from a shoulder injury recently, led the way for the Cavaliers with 20 points.
The Cavs nevertheless lead the Central Division after the Chicago Bulls slipped to a 98-84 defeat to the Indiana Pacers.
Solomon Hill scored 16 points and Ian Mahinmi managed a season-high 14 points and 11 rebounds as the Pacers finished strongly to secure their fourth consecutive win.
Atlantic Division leaders the Toronto Raptors continued their recent poor form by losing 104-93 to the Charlotte Hornets.
The Raptors have lost seven of their last eight games and were undone by 23-point games from Mo Williams and Al Jefferson, who also managed 13 rebounds.
Western Conference leaders the Golden State Warriors secured a 48th regular season victory for only the second time in their franchise history as they beat the Dallas Mavericks 104-89.
The Washington Wizards very nearly blew a 35-point lead against the Miami Heat but eventually secured a 99-97 win to record only their second victory in their last nine games.
A late fourth-quarter rally helped the Phoenix Suns force over-time against the Brooklyn Nets and they eventually sealed a 108-100 triumph.
Victor Oladipo scored 32 points and also managed 10 assists and five steals to lead the Orlando Magic to a 119-114 victory against the Sacramento Kings.
Kawhi Leonard grabbed 25 points and Tony Parker added 24 as the San Antonio Spurs were 120-111 victors against the Denver Nuggets.
Gordon Hayward scored 25 points as the Utah Jazz won 89-83 against the Philadelphia 76ers, while James Harden bagged 38 points to inspire the Houston Rockets to a 103-93 win against the Detroit Pistons.
Elsewhere, the Memphis Grizzlies won 97-90 against the Los Angeles Lakers and the Boston Celtics were 104-98 victors against the New Orleans Pelicans.