Stosur, who was the French Open runner-up in 2010, raced past Kimiko Date-Krumm 6-0, 6-2 in 64 minutes. Stosur won nearly two-thirds of the points in the match. She lost only 10 points in grabbing the lead in the first set and finished off five of her eight break chances.
Date-Krumm, at age 42, was the third oldest woman to appear in the singles main draw.
The start of play Tuesday was delayed 2 1/2 hours by rain and play had to be suspended for a considerable time in the afternoon. As a result, world No. 3 Victoria Azarenka had her first-round match pushed back to Wednesday.
No. 13-seeded Marion Bartoli fought off a challenge from Olga Govortsova 7-6 (10-8), 4-6, 7-5 in a match that took more than 3 hours. Bartoli won only two more points (131-129) on the day but advanced on her third break of the third set.
Other early Tuesday winners included Kristina Mladenovic, Silvia Soler-Espinosa, Yaroslava Shvedova, Marini Duque-Marino and Dominika Cibulkova.