Kyrie Irving, who had 26 points to lead Cleveland, made one of two free throws with 9.5 seconds left after Jordan Crawford and Garrett Temple missed jumpers for the Wizards. Crawford made two free throws with 8.5 seconds left to cut the lead to 86-84. Irving hit one of two, and Crawford missed a 3-pointer as time ran out.
Irving had 20 of his 26 points in the first half for the Cavaliers, who improved to 7-23. Two of their wins are against Washington, losers of eight straight.
Thompson had a season-high 15 points and 12 rebounds.
Crawford and Emeka Okafor led the Wizards with 17 points and Nene had 16.
Washington took a 79-73 lead with 6:20 to play, but Cleveland scored nine straight points to take an 82-79 lead with 3:37 left.
The Wizards were held scoreless for 4 1-2 minutes until Okafor hit a hook shot with 1:50 to play to cut the Cavaliers' lead to 82-81. Irving missed two free throws with 1:01 to play, and Okafor hit one of two with 46.2 seconds to play for an 82-all tie.
The Wizards broke on top 22-10 with 4:51 to play in the first quarter, thanks to Nene's 10 points. Cleveland's Irving had 12 of his 20 first-half points in the second quarter to help the Cavaliers grab a 45-43 halftime lead.
Washington started Shelvin Mack at the point. It was Mack's first NBA start. The second-year guard had been cut by the Wizards at the end of training camp, and re-signed on Tuesday after a strong stint in the D-League.
Mack was starting because Crawford was late to Wednesday's shootaround according to a team source. Before the game, Washington coach Randy Wittman said that Crawford was benched for a violation of team rules.
The Wizards scored 12 straight points to take a 62-53 lead with just over 7 minutes left in the third quarter with Mack hitting consecutive 3-pointers.
Irving missed all five of his field goal attempts in the third quarter, but hit two free throws to tie the score at 68-all to end the period.
NOTES: Shaun Livingston, who was waived after Saturday's game by the Wizards, was on the Cavaliers' bench after his Tuesday signing. Coach Byron Scott said he would evaluate Livingston, who's playing with his seventh NBA team, after Thursday's practice. ... Cleveland C Anderson Varejao missed his fourth game with a bruised right knee. Scott said he would be evaluated on Thursday. ... Temple, who signed on Tuesday, had two points.