Mo Williams scored 24 points, and LeBron James and Delonte West had 18 apiece for the Cavs (25-4).
Antawn Jamison hit a three-pointer with 1:40 left to put the Wizards ahead by seven points.
But James was fouled shooting a three and Cleveland's superstar, who had started 3-for-7 from the line, made three straight to pull Cleveland to 89-85. Williams then drew a charge on Jamison and hit a three-pointer to make it 89-88 with 1:03 to go.
Mike James missed for Washington and Jamison fouled out while battling Anderson Varejao for a rebound. Varejao made both free throws to give the Cavs a 90-88 lead, and Cleveland got the ball right back when Caron Butler was called for charging into Ben Wallace. The Wizards had to foul and Williams hit two free throws to make it 92-89.
The Wizards still had a chance to tie, but James, recently acquired from Memphis, missed a three-point try and West made one of two foul shots to ice it.
Washington (4-23) is off to the worst start in franchise history.
Spurs 91, Suns 90: : Roger Mason made a three-pointer from the corner at the buzzer to give visiting San Antonio (19-10) the victory.
The Spurs won their fourth straight. The Suns (16-12) led most of the afternoon, but never by more than eight in the second half.
Magic 88, Hornets 68: : Hedo Turkoglu scored 20 points to lead host Orlando (23-6) over New Orleans (16-9) in a matchup of division leaders. It was the Magic's sixth straight victory.
Chris Paul, the NBA steals leader (3.7 average), ended his league-record string of 108 games with at least one.
