Wall hit two free throws with 2 seconds to play and the Wizards survived a last-second 3-point attempt by Kobe Bryant.
Bryant had missed the previous two games with an ankle sprain, but he was back in the lineup along with Pau Gasol.
Gasol was playing for the first time in 21 contests after suffering from a foot problem.
Bryant had 21 points and 11 assists, but it was not enough to keep the Lakers from their second straight loss.
Trevor Ariza had 14 of his 25 points in the fourth period for Washington, which trailed by 18 points early in the second half.
Los Angeles leads Utah by only 1 1/2 games in the battle for the Western Conference's final spot in the playoffs.
Washington has won five of its last six.
2014: The Year in Music [PHOTOS]