The Lakers overcame a 13-point deficit to take a 97-94 lead with 5:46 left in the game. The 76ers responded with a 17-7 run to improve to 9-21 on the season.
The Lakers struggled with their shooting, making only 36.9% from the field while turning the ball over 22 times. The 76ers had only 11 miscues.
Guard Nick Young led the Lakers with 26 points off the bench, although he shot only 6 of 21 from the field and committed six turnovers.
Williams missed a crucial, wide-open three-point shot with 20.9 seconds left and the Lakers down 107-104.
Seven-foot Pau Gasol sat out with an upper respiratory infection. Forward Xavier Henry, who has been helping run the point, left late in the first quarter with a strained right knee. He'll have an MRI exam on Monday.
Point guard Kendall Marshall played his best game as a Laker with eight points and three assists.
The Lakers have lost five in a row to fall to 13-18 on the season. They'll have a chance to break the streak on Tuesday when they host the Milwaukee Bucks (6-24).
The Sixers (9-21) travel to Denver to play the Nuggets (14-15) on Wednesday.
The Lakers looked overmatched in the third quarter, getting outscored by the 76ers, 34-25, and trail by nine points entering the fourth quarter.
Power forward Jordan Hill gave the Lakers an inside force with 16 points and 12 rebounds. Guard Nick Young had score 18, but he's missed 11 of 14 shots. The Lakers as a team have shot only 34.9% from the field.
Philadelphia shot only 39.7% from the field but took 10 more shot attempts than the Lakers. The Sixers had 10 turnovers through three quarters, eight fewer than the Lakers 18.
The Lakers hit back-to-back three-point shots to close the second quarter to pull even with the Philadelphia at the half at 52.
Despite shooting only 34.9% from the field and committing 13 turnovers, the Lakers made up a nine-point deficit after Kendall Marshall and Nick Young each made shots from beyond the arc in the final 33.5 seconds of the quarter.