Nelson briefly got free, but came up empty on a 13-foot jumper, giving it back to Chicago.
Coming out of a timeout Mike Dunleavy got free on the wing and sank a 3-pointer to tie it with 13.4 seconds left.
Nelson dribbled the clock down, but couldn't get a shot off before time expired.
The Magic hovered above 55 percent shooting as they built as much as a 15-point lead in the third quarter.
Butler said the win was indicative of a style that hasn't gone away for the Bulls.
"We're grimy and we play as a team," he said. "There is no guy that doesn't give all the effort on every single play. Whenever you play like that, good things happen. The basketball gods will reward you."
NOTES: The Magic are now 0-11 without Vucevic this season, and 0-4 in overtime games. ... The Bulls recalled G Marquis Teague on Wednesday from the Iowa Energy of the NBA Development League.
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