Willie Green and Reggie Evans added 13 points each for the Sixers (5-10), who snapped a two-game losing streak at home and a four-game skid against the Wizards.
"Overall, we are a good defensive team," Evans said. "We help each other out. Overall, we played good, solid defense and that's the way to get wins."
Iguodala contributed eight points and 12 rebounds.
"We're not going to shoot well all the time, so we have to find other ways to win," Dalembert said.
Sixers coach Maurice Cheeks applauded his team's defense, especially in the second half.
"I thought our defense was the reason why we won that game," Cheeks said.
Caron Butler scored 20 points while Antawn Jamison had 16 points and 11 rebounds for Washington, which fell to 7-9. The Wizards are 4-4 since Gilbert Arenas went down with a knee injury expected to sideline him for three months.
"It wasn't a step back at all," Wizards coach Eddie Jordan said. "We just lost the game."
The game was tied at 68-all after three quarters and remained close throughout the remainder of regulation with neither team gaining a big advantage.
Despite playing in a half-empty arena, the crowd got loud as the Sixers snapped a 78-all tie and pulled ahead, 84-78, with 1:06 remaining. Dalembert hit a layup and two free throws during the key 6-0 spurt.
The Wizards pulled to 85-84 and had a chance to win the game on their final possession. Stevenson passed the ball to Young, but he missed a 26-foot 3-pointer with 1.9 seconds left. The ball caromed away, and the buzzer sounded before the Wizards could put up another shot.
"I thought it was a great shot," Young said. "It felt good coming out of my hand. It just didn't go down."
Washington overcame an early 11-point deficit to take a 43-42 lead at halftime.
Jamison had 12 points and Brendan Haywood blocked four shots in a five-minute span as the Wizards surged ahead.
Wizards assistant coach Randy Ayers was the 76ers head coach for part of the 2003-04 season. ... Jamison entered the game averaging a career-high 9.9 rebounds. ... The Wizards bench outscored the Sixers bench 19-14. ... Kyle Korver is 3-for-19 from the field over his last two games. ... The Wizards committed 18 turnovers while the 76ers had a season-low eight.