Stosur struggled with her usually dominating serve and fell to World No. 83 OIga Govortsova of Belarus in the second round of the hard-court event at Stanford University, which was a tune-up for Stosur for the upcoming U.S. Open, an event she won in 2011.
Govortsova moved on and will face American Coco Vandeweghe, who ousted Monica Niculescu 6-0, 6-3.
Seeded winners Tuesday included No. 6 Varvara Lepchenko of the United States, who defeated Michelle Larcher de Brito of Portugal, 6-2, 6-4. Seventh-seeded Urszula Radwanska of Poland dispatched American Christina McHale, 6-1, 6-3.