The Nuggets fell behind by as many as 11 points in the first half before rallying for their third straight win.
Washington failed in its bid to produce back-to-back victories for the first time this season. The Wizards posted their just second triumph of the season over Oklahoma City on Wednesday.
Jordan Crawford brought Washington within two with 10 seconds remaining by making two free throws, but Harrington ended the Wizards' hopes with his dunk for the last of his game-high 29 points.
Nick Young had 25 points for the Wizards.