Miami has dropped three in a row for the first time in two years.
Washington took a 43-18 lead after one quarter, led by 30 in the second period and survived a Miami comeback that brought the Heat to within nine heading into the final 12 minutes.
Dwyane Wade returned to the Miami lineup after missing time with sore knees. He played 33 minutes, but scored only eight points.
Wall, meanwhile, led Washington to a 54 percent shooting performance and had 25 points Nene and Bradley Beal both produced 19 points while Trevor Booker had 13
The Wizards have won two straight to draw within a game of the .500 mark. The three Miami losses have come at the start of a six-game road trip.