The Magic ended an eight-game losing streak and won for just the 19th time this season -- the second fewest number of victories in the NBA.
Orlando led by 15 late in the first half only to have Washington make up all its deficit and edge in front early in the fourth period.
E'Twaun Moore put the Magic back ahead for good with 8:33 to play on a jumper and Harris hit a key 3-point play with 3:11 remaining that boosted the Orlando lead to six. Three free throws from Harris in the final 14 seconds secured the victory.
Harris hit 11-of-19 from the field and grabbed 11 rebounds. Maurice Harkless added 18 points and Moore finished with 15.
The Wizards missed out on a chance for what would have been their eighth road win of the season. Instead, they fell for the 29th time in 36 games away from home.
John Wall led Washington with 35 points.