Both women had come through testing three-set battles yesterday [Saturday] and entered today's [Sunday] final with the Australian slightly holding the upper hand in past meetings, having won three of five.
However, it was the Dane who prevailed, winning 6-2 4-6 7-5 to add to the title she won in Seoul last month.
Stosur has not won a title since she was crowned US Open champion more than a year ago and was inconsistent, her four aces accompanied by seven double faults.
Neither did she have any success with her second serve making her reliant on her first and only six of 15 break points were converted.
In contrast Wozniacki was consistent if not spectacular with greater success on her serve as well as taking greater advantage of her break point opportunities.
Wozniacki said on Twitter: "Won in Moscow today! 20th tournament title:) #excited."
The outcome of the men's final between Thomaz Bellucci and Andreas Seppi was similarly unpredictable before the latter finally prevailed 3-6 7-6 (7/3) 6-3.
The Italian second seed had lost only four games in his semi-final victory against Malek Jaziri yesterday while Bellucci, seeded four, had come through a tough three-set encounter with Ivo Karlovic.
The fact he had expended far less energy yesterday was always going to favour Seppi and so it proved as he came through in two hours and 12 minutes.
Bellucci served 13 aces, 11 more than Seppi and achieved far more success all-round on his serve.
While the Brazilian took far more advantage of his break point opportunities - converting all three - it was Seppi's all-round game that led to victory.
Boyfriend and world number one golfer Rory McIlroy Tweeted: "20th WTA title for @CaroWozniacki!!!! So happy and proud of her!!!"