The Hawks overcame a 27-point deficit in the second quarter as well as the second triple-double in as many nights for Boston's Rajon Rondo.
Kyle Korver hit eight 3-pointers for Atlanta, which trailed 48-21 midway through the second period.
Horford made two free throws with a minute left in the fourth quarter to tie it and neither team could score again. There was also no scoring for the final 1:34 of the first overtime after Atlanta's Josh Smith tied it at 107-107 on a dunk shot.
Atlanta held the Celtics scoreless for the first 3:41 of the second overtime. Boston lost its sixth straight game, its longest skid in six seasons. Atlanta has won three in a row.
Korver scored 27 points to lead the Hawks, 24 of them coming in the second half. Horford chipped in 24 points and Jeff Teague had 23.
Rondo scored 16 points along with 11 assists and 10 rebounds. Kevin Garnett fouled out early in the second extra period after scoring 24 points.