The Wizards grabbed the lead with a 12-1 run in the final minutes at the Veterans Memorial Arena in Jacksonville, Florida.
Eric Gordon had 15 points for New Orleans, which led 49-44 at halftime. Ryan Anderson scored 14, and Jimmer Fredette finished with 13 points.
Wall went 5 for 10 from the field. He also had nine of Washington's 20 turnovers.
Nene added 10 points for the Wizards on the same day the NBA announced he was suspended for one regular-season game for leaving the bench area during an altercation between Paul Pierce and Chicago's Joakim Noah.
Noah was fined $15,000 for initiating the altercation in Monday night's exhibition game in Chicago by pushing Pierce in the chest, and Pierce was fined $15,000 for hitting Noah in the forehead with his left index finger.
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