The Bulls, playing their fourth straight game without reigning NBA MVP Derrick Rose, opened an 18-point lead early in the second half only to see Boston move in front by a point in the fourth period.
Deng led Chicago on a 19-9 run to finish the game, getting the surge started with a 3-pointer that gave the Bulls a 75-71 lead with 7:28 to play.
Chicago improved its home record to 11-1. The Bulls are 3-1 since Rose was first held out of the lineup with a sore back.
He briefly took part during Chicago's shootaround Thursday, but his back had not responded to treatment to the point he could play.
Kevin Garnett scored 18 points for Boston, which played on the road for just the 10th time this season.
Golden State is the only team in the NBA with fewer road games, having played nine.