Thaddeus Young added 18 points and 13 points for the 76ers, who had played a pair of stinkers since being mathematically eliminated from the playoffs but handled the Wizards, who had made catching Philadelphia a very public goal to make up for a 4-28 start.
John Wall scored 24 points for the Wizards, who have lost four straight and trail the 76ers by 3½ games with two to play in the race - if it can really be called that - for top non-playoff team in the Eastern Conference.
The 76ers have been a disinterested competitor for the Wizards, and they still could be caught by the 10th-place Toronto Raptors. Asked before the game if the tussle for ninth was on his radar, Philadelphia coach Doug Collins shrugged and said: "You know, ninth, 10th - I mean, that's out of the playoffs."
The 76ers had lost three straight, including two by an average of 22 points since their playoff hopes ended, and Collins' future with the organization is in question.
"When you're mathematically eliminated," Collins said before the game, "it's tough to get guys playing at the highest of levels. ... It's human nature: You're fighting, you're fighting, you're fighting, and all of a sudden it's like, 'We're out of the playoffs.'"
Nevertheless, Holiday bounced back after a pair of bad games and made 8 of 17 shots and also had seven assists. Five 76ers scored in double figures, but Evan Turner didn't join in the fun, however, going 0 for 11 from the field.
The Wizards had been strong at home since Wall returned from a knee injury. They finished 22-19 at the Verizon Center, including 18-6 with Wall.
Washington started well Friday, with assists on their first eight field goals, including a no-look, nonchalant pass from Nene to Wall for a layup. Wall also dribbled down the clock and maneuvered through traffic for a falling-down layup at the end of the first quarter.
No play exemplified the 76ers' end-of-season funk better than Dorell Wright's 3-point attempt late in the first quarter. The ball slipped out of his hands and went backward with no one touching it, landing in the front row of seats some 30 feet from the basket.
But, after the Wizards built a 13-point lead in the second quarter, the 76ers closed the half with a 20-8 run to make it a one-point game at the break. Arnett Moultrie's follow dunk early in the fourth quarter pushed the 76ers' lead into double digits, and the Wizards didn't get closer than seven the rest of the way.