Washington scored only two points over the final 4:16 after drawing within four.
The Magic won their fourth straight and have captured five out of six.
Redick finished with 17 points off the bench while both Arron Afflalo and E'Twaun Moore had 15 for Orlando. The Magic hit only 41 percent of their shots, but had 10 more rebounds than did Washington and hit eight more free throws.
Orlando's Glen Davis left the game in the fourth quarter after taking a hit on the shoulder from Washington's Emeka Okafor.
Nene paced the Wizards with 20 points, but Washington fell for the fifth straight game. The Wizards have won just three times, two fewer than any other club in the NBA.
Orlando has defeated Washington in 10 of their last 11 meetings.
2014: The Year in Music [PHOTOS]