The American finished with a two-run time of 1.34:60. Kalle Palander of Finland was second and Mario Matt of Austria third.
Miller had won two giant slaloms this season but this victory on the Sonnenwiese course was his first slalom win in more than two years.
In the overall cup standings, Hermann Maier of Austria leads with 1,054 points, followed by fellow Austrian Benjamin Raich with 985 and Miller at 984.
Celebrity Families of 2014 [PHOTOS]