LeBron James led the Heat (12-4) with 26 points, 13 rebounds, 11 assists, three steals and two blocks (and three turnovers).
But the Wizards (2-13) got a balanced effort and a strong performance from their bench to hold off a late comeback and win 105-101.
Jordan Crawford led Washington with 22 points and Kevin Seraphin had 16 points and 10 rebounds, including a big fourth quarter.
James missed a 3-pointer on the Heat's last possession as the team trailed 104-101, and it was preceded by a series of Heat misses with the game in the balance in the last few minutes.
Dwyane Wade had 24 points and Chris Bosh added 20 points and 12 rebounds.
Mario Chalmers left the game with a hand injury but it is not considered serious. The Heat were also without Norris Cole in the game, leaving the team with a prototypical point guard for much of it. Terrell Harris started the second half and did some ball handling, as well as defending the opposing point guard for Miami.
The Wizards scored 100 points for just the 4th time this season.