Dukes hit his slam during a six-run fifth that gave the Nationals a 9-1 lead and Willingham added a three-run blast in the eighth. Willingham also homered in the fourth as part of Washington's 14-hit attack.
The Cubs fell nine games behind St. Louis in the National League Central, the largest margin between a division leader and a second-place team.
Garrett Mock (5-3) lasted 5 2/3 innings to get the easy win. He allowed four runs on seven hits while striking out six.
Washington roughed up Carlos Zambrano (7-5) for eight runs on seven hits in 4 1/3 innings.
Zambrano was activated from the disabled list to make the start. He had last pitched Aug. 1, after which he complained of back spasms.
Copyright 2009 by United Press International.