An inspired Schiavone tamed Stosur's greater power to win 6-4 7-6, completing victory when Stosur mishit a backhand.
Both women were making their grand slam final debuts but it was the 29-year-old Schiavone who seized her chance with some tremendous attacking play.
After dropping the first set Stosur moved 4-1 ahead in the second but the tenacious Schiavone stormed back to take the set into a tiebreak and moved 6-2 ahead with a superb volley.
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She needed just one chance to take the title, celebrating by before falling onto her back and kissing the Court Philippe Chatrier Court before climbing into the stands to embrace her entourage.
