The Hawks snapped a two-game skid, getting 23 points, eight assists and seven rebounds from Josh Smith. Zaza Pachulia added a career-best seven assists.
Atlanta did not take the lead for good until late in the third period, during which Washington scored only 10 points.
Washington has two games left on its six-game road trip, on which it is 1-3.
Ray Liotta sues skin care company over use of likeness
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