Deng's basket off an assist from Joakim Noah proved to be the game-winner in an exciting final minute that played out after the Bulls had erased a 19-point deficit.
Chicago went up 74-73 when Derrick Rose scored on a driving layup with 9.9 seconds left.
Atlanta's Al Horford responded at the other end by making 1-of-2 foul shots to tie the score with 7.7 seconds remaining.
That set up the decisive play, in which Noah found Deng down low for an easy layup and a 76-74 Bulls lead.
The Hawks had one last chance but Joe Johnson missed a 3-pointer as the horn sounded, and Chicago hung on for its fourth straight win.
Derrick Rose finished with 30 points and seven assists and Deng had 21 points and eight rebounds for the Bulls.
Horford had 16 points to lead four Hawks starters scoring in double figures. Horford grabbed seven rebounds.