Andre Iguodala and Louis Williams each had 13 points for Philadelphia, which missed 13 of 33 free throws in the game.
The Wizards never trailed until two free throws by Andre Miller gave the 76ers a 60-59 edge with 1:30 left in the third period.
Washington led 66-60 at the end of three quarters but went on a 7-2 run to start the fourth quarter to take a 73-62 advantage with 8:20 remaining on two free throws by Andray Blatche.
The 76ers rallied behind Williams to close to 77-75 with three minutes left, but a three-point play by rookie Nick Young ended the threat.
Philadelphia center Sam Dalembert, recovering from a stress fracture in his left foot, missed his second straight game. Coach Maurice Cheeks said Dalembert will not travel to Utah for the 76ers' next game on Wednesday.
"We'll keep monitoring him, and if he's still sore after 10 days, then we'll be a lot more concerned," Cheeks said.