Carlos Boozer scored 31 points and had 11 rebounds for the Bulls, who held on down the stretch after taking an 18-point lead during the third quarter.
Orlando climbed within two on a 3-pointer by Arron Afflalo with 46 seconds to play and the Magic got the ball back with a chance to tie or take the lead.
Jameer Nelson had one attempt blocked out of bounds and his second jump shot with 5 seconds left misfired.
Deng grabbed the rebound and was immediately fouled. His free throws gave Chicago a 96-92 lead and made Nelson's layup at the buzzer meaningless.
Deng scored 23 points while Taj Gibson added 21 and 11 rebounds.
Nelson finished with a career-best 32 points, helped along by six 3-pointers.
Notable deaths of 2014 [PHOTOS]