In what amounts to a blow for her Australian Open hopes, Stosur lost 7-6 (7/4) 7-5, following on from the defeat suffered by Caroline Wozniacki, who was beaten by Ksenia Pervak.
The former world number one was a 2-6 6-3 7-6 (7/1) loser, meaning she too has lost out on some valuable court time ahead of the first grand slam of 2013.
Also in action in the women's competition were Sabine Lisicki, a two-set winner over Lucie Safarova, Angelique Kerber who beat Anna Tatishvili and Alize Cornet, a victor against Bojana Bobusic.
Sara Errani looked good in beating Olga Puchkova 6-1 6-3, while the likes of Sloane Stephens and Monica Puig also made easy progress.
Florian Mayer was victorious in the men's competition, a 6-4 6-4 winner over Santiago Giraldo, while Jarkko Nieminen went the distance against Julien Benneteau.
Fifth seed Kei Nishikori got the better of home favourite Marinko Matosevic, with Marcos Baghdatis doing the same against Benjamin Mitchell.