Wozniacki defeated Greta Arn 6-1, 6-3, dropping serve just once. She had Arn on the defensive throughout the match, forcing 15 break-point situations and finishing off five of them.
Stosur was dumped by Julia Goerges 7-5, 6-3 after losing four service games.
In other upsets, No. 10-seeded Svetlana Kuznetsova fell 6-3, 7-5 to Andrea Petkovic; Kaia Kanepi ousted 13th-seeded Shahar Peer 6-3, 7-6 (7-5); and U.S. qualifier Coco Vandeweghe also advanced to the third round, knocking off 14th-seeded Aravane Rezai 6-4, 6-4, amassing three service breaks in each set.
Playing more to form, second-seeded Vera Zvonareva topped Sara Errani 6-3, 6-3 and No. 5-seeded Francesca Schiavone got past Alexandra Dulgheru 7-5, 6-3 while seventh-seeded Elena Dementieva routed Yaroslava Shvedova 6-0, 6-1 in 51 minutes with six service breaks.
Victoria Azarenka, seeded eighth, took out Lucie Safarova 6-1, 6-3; No. 11 Marion Bartoli defeated Ana Ivanovic 6-2, 6-1; and 16th-seeded Anastasia Pavlyuchenkova dumped Kateryna Bondarenko 6-2, 6-1.
Kimiko Date Krumm marked her 40th birthday Tuesday by advancing to the third round. She was ahead 2-6, 6-0, 4-0 when Daniela Hantuchova retired with a shoulder injury.
Also Flavia Panetta defeated Maria Kirilenko 6-3, 4-6, 6-3; and Roberta Vinci stopped Tsvetana Pironkova 6-4, 6-2.