The Hawks jumped to a 19-4 lead and, although the Wizards climbed back within three in the second period, Atlanta rebuilt a 13-point halftime edge. Atlanta was out front by as many as 22 points in the fourth quarter.
Johnson led the Hawks with 18 points and Williams had 17. Josh Smith pitched in 15 points to go with 10 rebounds and Al Horford had 11 points and 10 boards.
Atlanta has won its opening two games of the season and Washington has lost its first two.
Johnson had four of Atlanta's nine 3-pointers. The Hawks seized 13 more rebounds than did the Wizards.