James - who was unable to prevent the Lakers from a 127-119 loss - now has a career total of 36,947 points and passed Karl Malone's record of 36,928 points.
James hit three three pointers, a dunk and a lay-up in the second quarter to go past Malone's record.
The only player to have scored more points than James is Kareem Abdul-Jabbar who has a total of 38,387.
The 37-year-old said it will take some time to reflect on the achievement after not being able to inspire the Lakers to victory.
"At some point I'll be able to look back at this moment, but right now the feeling I have, I can't separate it [from the loss]," James said.
The Wizards' 16-point win meant that they snapped a run of six defeats.
James was also asked about the possibility of breaking Abdul-Jabbar's record but the
American is refusing to be drawn in.
James said: "I will not allow myself to think about it.
"I've always just played the game the way I've been playing it over the years, and these things have just happened organically by just going out and playing the game the right way.
"I hope to accomplish that at some point in my career, but I won't think about it too much."
In other NBA results, the Minnesota Timberwolves overcame the Milwaukee Bucks 138-119 while the Cleveland Cavaliers beat the DetroitPistons 113-109.
The Charlotte Hornets were also victorious with a 129-108 win against Dallas Mavericks.