Alex Chiasson's second-period goal proved to be the game-winner and Erik Cole also scored as the Stars reached the win column for the first time following a season-opening loss to Florida.
The Capitals' only tally came from Alex Ovechkin, who notched his fourth of the season on a power-play.
Braden Holtby stopped 19-of-21 shots for Washington.
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'
Beyonce flaunts bikini body, Blue Ivy in vacation pics