Victor Oladipo had a career-high 35 points and Jameer Nelson added 31 points and 10 assists for Orlando. Tobias Harris added 22 points and 16 rebounds.
"I was more mad than exhausted," said Oladipo, who played a team-high 57 minutes. "I'm more mad than exhausted right now. But it's a short turnaround, so you have to have a short-term memory."
What made Orlando's effort even more surprising is that it played without starters Arron Afflalo and Nik Vucevic. Afflalo missed his third straight game with a strained right foot, and Vucevic was out for the fifth straight with a concussion.
During their recent road trip, the Magic were tripped up by those injuries.
Despite losing by an average of 20 points during the trip, coach Jacque Vaughn continually lauded his team's improvement throughout. He did again after Wednesday's loss.
"You feel for the guys, you want them to get a victory underneath them. But we got better tonight," Vaughn said.
In a game that didn't see either team take more than an four-point lead in any of the overtime periods, the Magic went ahead 125-122 in the third OT on a 3-pointer by Harris.
But Chicago kept chipping away, and eventually took the lead for good, 126-125, on a jumper by Tony Snell.
The Bulls had a 119-116 lead in the second overtime on a tip-in by Noah.
After several empty possessions on both ends, Davis tied it on a straightway 3 with just 4.2 seconds left.
Noah got free on a drive on the other end, but was fouled.
The Bulls then failed to get up a shot.
The Magic controlled the early pace of first overtime and took a 111-108 lead on a free-throw by Harris with 1:22 remaining.
But the Bulls committed their 17th turnover of the night on a bad pass by Noah with less than a minute to play, prompting a Magic timeout.