Dwyane Wade scored 13 of his 22 points in the fourth quarter in front of a crowd of 19,657 at the AmericanAirlines Arena.
“This was a game that showed some growth,” said Miami coach Erik Spoelstra.
James also tallied eight assists and seven rebounds, while Chris Bosh added 22 points and seven rebounds for the Heat, who haven’t lost four in a row since a five-game losing streak in 2011.
Spoelstra was especially pleased to see James back in form after a couple of off nights for the 2013 playoff MVP.
“He takes it to heart,” Spoelstra said, “and I love to see that leadership.
“I felt good about this game the minute LeBron walked into the gym.”
Miami now trails the Indiana Pacers by just one game for first place in the Eastern Conference standings.
Bradley Beal scored 18 points, Martell Webster scored 17 and Marcin Gortat finished with 14 points and 18 rebounds for the Wizards, who have won eight of their last 10 games.
The Heat are back on track at home after losing all three games on a recent road trip to Houston, San Antonio and Chicago.
Washington led 84-83 following Drew Gooden’s layup just past the halfway mark of the fourth, but Wade answered with a three-point play to key a 12-0 run from the Heat.
Bosh buried a three-pointer in the burst before Wade capped it with a layup for a 95-84 lead with just over three minutes left in the fourth.
Miami held Washington to just a couple of field goals the rest of the way to secure the victory.
The Heat are now 25-4 at home and are unbeaten in their last six at the AmericanAirlines Arena.
The Wizards had their five game road win streak snapped and next face Charlotte and Orlando.