DeShawn Stevenson inbounded the ball to Horford, who scored on a layup to pull the Hawks even with 19.5 seconds remaining.
Nene had 12 points in his season debut, though he didn't start. He missed the first nine games with a left foot injury. Trevor Ariza had 12 points and a game-high 15 rebounds for the Wizards, including a 3-pointer in overtime.
The Wizards had a 58-37 advantage in rebounds.
"For the first time we really played," Nene said. "We played good.
"If we can play like that against the Hawks, we can play against anybody."
With Washington leading 87-86, Nene stripped the ball from Smith, setting up a layup by Price which pushed the lead to three points. A layup by Teague cut the Wizards' lead to 89-88. Horford missed a jumper for Atlanta. Nene made one of two free throws with 10.3 seconds left, giving Washington a 90-88 lead.
Nene fouled Harris with 3.7 seconds remaining. Harris made both free throws to tie the game at 90-all. Shaun Livingston missed a 3-pointer to force the overtime.
There were 20 lead changes in the game, including 10 in the first half. The Hawks led 50-47 at the break and stretched the lead to 11 points at 66-55 on back-to-back 3-pointers by Korver. The Wizards answered with nine straight points, seven on free throws.
Notes: The Hawks paid a halftime tribute to former star forward Dan Roundfield, who played for the Pistons, Indiana, Atlanta and Washington. Roundfield was 59 when he drowned on Aug. 6 while helping his wife, Bernie, in rough water near Aruba. Roundfield's wife and other family members attended the ceremony. ... Horford made only 1 of 10 free throws. ... Wizards F Trevor Booker was held out with a strained right knee. ... Wizards rookie Bradley Beal fouled out in the first minute of overtime with six points and four assists. ... Drew said a flu virus that went through the team no longer is an issue. ... The Hawks have won nine straight over the Wizards in Atlanta. Washington's last win at Philips Arena was on Jan. 11, 2008.