The Magic led 70-65 when the Bulls started their decisive run late in the third quarter. Deng tied the game with a jumper with 10:58 to play. Later, Robinson capped the run with a layup in transition.
"I think we wanted it more," Robinson said. "I think at the end we were more gritty. Coach said whatever it takes to get the win. So tonight, we had to gut it out."
Orlando trimmed the lead to four on Affalo's 3 in the final minute, but Chicago held on down the stretch. Gibson's dunk and free throw with 39 seconds remaining iced it for the Bulls.
The Magic pushed the lead to seven in the second quarter behind seven points from Moore before Richard Hamilton closed the lead to 48-45 with a pull-up jumper in transition to close the first half.
J.J. Redick continued his hot shooting early with a 3-pointer and a midrange jumper during the spree. Redick hit 16 of 25 shots in Orlando's first two games.
After making his first two shots, Redick hit just one of the next seven before hitting a 3-pointer in the fourth quarter, with Butler sticking to him for most of the second half.
"We just found a way," Noah said. "We fought hard at the end. Jimmy (Butler) gave us a great spark."
The Bulls needed the win after losing to New Orleans on Saturday and with Oklahoma City visiting the United Center on Thursday. The Bulls have not lost two straight at home since a five-game skid from March 1 to 19, 2010.
"This was a tough game," Deng said. "They're playing well and we lost our last game. It's one of those we needed to win. You don't want to lose two, then we've got Oklahoma (City) coming in. The fourth quarter was really good for the team."
NOTES: Orlando point guard Jameer Nelson missed his second straight game because of a strained right hamstring and groin. He's day to day. ... While the game was announced as a sellout, there were many more empty seats than usual at the United Center. Beside the elections and the absence of Bulls star Derrick Rose, the weather was cold and drizzly in Chicago. ... Bulls Hall of Famer Scottie Pippen sat courtside with his wife during the game after playing basketball with President Obama earlier in the day. ... Despite the loss, Orlando was 8 for 19 from 3-point range. The Magic entered the game with a 53.8 percent mark behind the arc.