Williams scored goals 3 minutes apart late in the first period, giving Los Angeles a 2-1 lead.
The Stars' Rich Peverley got the only goal of the second period, forging a 2-2 tie, but Doughty put the Kings ahead to stay 4:42 into the final period when he took a pass from Williams and tucked it inside the post.
Kyle Clifford made it 4-2 later in the period and Matt Greene added an empty-netter for Los Angeles, which won for the fifth win in six games.
Tyler Seguin notched a goal and an assist for Dallas, which fell for third time in four contests.
Dan Ellis made 29 saves for the Stars.