Horford's two free throws with six seconds left in the fourth period brought about the extra session and the Hawks took a four-point lead with 1:34 to go in the overtime.
Trevor Booker then hit consecutive baskets for the Wizards to tie it, the second of them coming on a reverse layup with just two seconds to play.
After a time out, Horford took a cross-court lob pass from Pero Antic and nailed the winning basket. The Wizards lost their third straight.
Horford equaled his career best with 34 points, hitting 15-of-23 shots. He also grabbed 14 rebounds.
Booker led Washington with 24 points and 14 rebounds. Washington has lost in each of its last 11 trips to Atlanta. The Wizards' last victory on the Hawks' home court came on Jan. 11, 2008.