"It was better, but it's not what it needs to be," Bulls coach Tom Thibodeau said. "We had good offensive energy, and not the necessary defensive energy. It was better, but we still have to do much better than we did tonight."
The Bulls led by as many as 18 in the third quarter before a 13-6 run by the Magic trimmed it to 82-71 entering the fourth.
Despite its size disadvantage, Orlando held its own on the boards and stayed close down the stretch.
Nelson scored five straight points to cut the deficit to six and Vucevic dropped in back-to-back layups that trimmed it to 86-84 with 5:12 left.
Two shaky Magic possessions and a turnover allowed the Bulls to respond with eight straight points, pushing the lead to 94-84.
J.J. Redick hit a 3-pointer and a Vucevic got a dunk to give Orlando life, and following a Bulls miss, Redick found Afflalo, who swished a 3-pointer from the corner to cut it to 94-92 with 46.3 seconds on the clock.
The Bulls came up empty on their ensuing possession, and Gibson blocked a Nelson layup attempt out of bounds with only 11.3 remaining. Nelson then found a lane to the basket, but put up an off-balance, leaning floater that bounced off the rim.
Deng rebounded the miss and knocked down two free throws with 4.2 left to secure the win.
The Bulls' starting frontcourt held a 37-15 scoring advantage over the Magic in the first half, helping the Bulls build a 54-46 halftime lead. Boozer was the most active, scoring 17 points on 8-of-11 shooting. The Bulls also held a 20-14 edge on points in the paint.
"It was big," Gibson said. "We were down a lot of guys and we have guys banged up. We just have to come together as a whole and try to take each game one at a time. The way we got it down in the second half in in particular in the last quarter speaks volumes."
Notes: Vucevic's double-double was his 14th of the season. ... Bulls F Vladimir Radmanovic missed his third consecutive game with flu-like symptoms. ... Magic G E'Twaun Moore sat out his third straight game with a sprained left elbow.
Follow Kyle Hightower on Twitter at http://www.twitter.com/khightower .