The Hawks trailed, 31-21, after one quarter, and 52-46 at the half, but outscored Washington, 27-15, in the third quarter to carry a four-point advantage into the final stanza.
Anthony Johnson had 19 points, three rebounds, and four assists; while Josh Smith and Salim Stoudamire scored 13 points apiece for the Hawks, who had dropped 10 of their last 11 games against Washington before Wednesday night's victory, and snapped a six-game losing streak overall.
They won without their top scorer, Joe Johnson, who is out with a calf injury.
Gilbert Arenas led Washington with 28 points, five rebounds, four assists, and four steals.
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