Luol Deng scored eight of his team-high 23 in the fourth quarter where reserve Nate Robinson also provided a spark to quickly erase a three-point deficit and take the game by the horns.
"I think we wanted it more," Robinson said after scoring seven of his 11 points in the final period.
"Coach said to do whatever it takes to get the win."
The Bulls were able to improve to 3-1 this season where they are without 2010-11 MVP Derrick Rose, sidelined indefinitely after tearing knee ligaments during last season's play-offs.
The Magic, rebuilding following the trade of Dwight Howard to the Los Angeles Lakers, suffered their first loss of the season despite 28 points from Arron Afflalo.
In a tightly contested game, Orlando grabbed a 71-68 lead after the third quarter before Chicago opened the fourth with a 12-2 run.
Robinson and Deng traded critical jump shots during the scoring run to position the Bulls for victory.
Joakim Noah had 20 points, nine rebounds and five blocks for the Bulls while Carlos Boozer added 12 points and eight rebounds.
Glen Davis, who had been carrying the Orlando offense and entered the game with a 25.5 points per game, could not find his range and made just 7 of 22 shots.
He ended up with 16 points and 10 rebounds.
The Magic are playing through injuries and were without point guard Jameer Nelson who missed a second successive game with leg injuries. Forward Hedo Turkoglu is also out after breaking his hand in the season opener.
"There's no All-Stars on this team," Davis said.
"Any night, anybody can be our star. We need to help each other, and tonight we kind of got away from it a little bit."
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