The Wizards lost their fifth in a row and remained stuck on seven victories for the season, second fewest in the NBA ahead of only Charlotte.
Maurice Evans hit a 3-point shot for Washington with 6:59 to play that tied it at 83-83, but Nelson and Anderson then hit their long-range shots to push the Magic in front by six.
Anderson had four 3-point shots among his 23 points and he also grabbed 15 rebounds. Nelson scored 12 points, while Dwight Howard had 14 points and 12 boards. There were seven Orlando players in double figures.
Orlando overcame a 33-point effort by John Wall, the second-largest point total of his second NBA season.