James had 33 points with 15 rebounds and eight assists in 45 minutes for the Cavs, who added four players in an 11-player blockbuster deal on Thursday but couldn't dress Ben Wallace, Wally Szczerbiak, Joe Smith or Delonte West.
James could have used some help, but as always, he did whatever Cleveland needed.
Damon Jones scored a season-high 27 points for the Cavs, who were forced to sign Billy Thomas and Kaniel Dickens from the Developmental League to 10-day contracts just so they'd have enough players to meet the league's required eight for a game.
After James dropped his free throws, Washington went to DeShawn Stevenson for the final shot. He drove the right side and lofted a high layup that bounced off the top of the backboard and then the front of the rim.
James grabbed the ball and fired it into the scoreboard in celebration.
Darius Songalia scored 19 points and Stevenson 18 to lead the Wizards, who have lost 10 of 11.
The Cavaliers went up 88-85 on Devin Brown's dunk with 1:42 to play, but Zydrunas Ilgauskas fouled Brendan Haywood, who made two foul shots to bring the Wizards within one. After a Cleveland turnover, Ilgauskas was whistled for another foul and Stevenson's two free throws put the Wizards up 89-88.
James missed a tough 3-pointer from the corner, but the Wizards couldn't convert and gave Cleveland's All-Star another chance. He was fouled on a drive in the lane and calmly made both free throws.