The Magic ended a six-game losing streak and won on the road for just the second time in 12 tries.
Two free throws by Kemba Walker brought Charlotte within five points heading into the closing 60 seconds, but Nelson then hit a layup and, after a miss by the Bobcats, converted a pair of foul shots to wrap up the win.
Charlotte had been trying for its first three-game win streak of the season.
Nelson and Glen Davis both scored 17 points for the Magic with Davis adding 12 rebounds. Arron Afflalo contributed 16 points.
Gerald Henderson was Charlotte's leading scorer, but he produced just 12 points while making a mere 3-of-14 from the field.