On the eve of the French Open, Stosur, who has been the Australian number one since October 2008, recovered from a shaky start to boost her confidence ahead of the claycourt grand slam in Paris, where she reached the final in 2010.
Sixth seed Stosur, 33, made a slow start, falling 3-1 behind in the opening set, which Gavrilova, the seventh seed, claimed after another break in the 11th game.
Stosur's power was then too much to handle for 23-year-old Gavrilova, who offered some resistance in the second set but was completely outplayed in the decider.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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