Stosur fell early Wednesday to Arantxa Rus, No. 72 in the world and without a WTA title. Rus converted three third-set break opportunities for a 6-2, 0-6, 6-4 second-round win over Stosur.
Grass courts aren't the favorite for Stosur, the defending U.S. Open champion, and Rus capitalized on that. She had three breaks in grabbing the first set but managed to win just seven points in the second set as Stosur evened the match.
Rus found her footing again in the third set and made the most of her break chances to advance.
Tamira Paszek took a tight first-round battle from Wozniacki 5-7, 7-6 (7-4), 6-4, finishing the upset with a forehand winner for her seventh break of the day.
Wozniacki also had seven breaks, won more points (117-115) and had fewer unforced errors (22-41), but Paszek fired off 54 winners, including 15 in the final set, to advance.
That match was on Center Court and was suspended for a time because of rain. The roof was closed, however, and the match continued. Play on the outdoors courts at Wimbledon was suspended for several hours after an early round of matches.
With that delay there were many matches that didn't get completed Wednesday. That included a second-round match for No. 1-seeded Maria Sharapova, who was leading Tsvetana Pironkova 7-6 (7-3), 3-1 and about to serve when play was stopped. Sharapova fought off five set points in the first set.
One highly seeded player who didn't have problems Wednesday was No. 3 Agnieszka Radwanska, who dispatched Elena Vesnina 6-2, 6-1 in 56 minutes.
Other seeded players claiming second-round wins were 12th-seeded Vera Zvonareva and No. 15-seeded Sabine Lisicki, but Sorana Cirstea eliminated No. 11 Li Na 6-3, 6-4 and Sloane Stephens ousted 23rd-seeded Petra Cetkovska 7-6 (8-6), 4-6, 6-3.
Heather Watson cheered British fans with a 6-1, 6-4 win over Jamie Hampton that put her into the third round. Also picking up second-round decisions were No. 17 Maria Kirilenko, 30th-seeded Peng Shuai, Kim Clijsters, Hsieh Su-Wei and qualifier Camila Giorgi.
Several first-round matches were suspended Tuesday and completed Wednesday. That included 10th-seeded Sara Errani, who was at match point when her match with Coco Vandeweghe was suspended. They warmed up Wednesday and Vandeweghe committed a double fault, ending the match.
Klara Zakopalova finished off an upset of 13th-seeded Dominika Cibulkova 6-4, 6-1 but No. 14-seeded Ana Ivanovic beat Maria Jose Maria Sanchez 6-3, 3-6, 6-3 and 22nd-seded Julia Goerges breezed past Shahar Peer 6-3, 6-2.
Also advancing out of the first round were Alize Cornet, Kateryna Bondarenko, Olga Govortsova and Anastasiya Yakimova.