After needing three breaks to escape with the first set, Stosur fought off all six break points she saw in the second of a 7-5, 6-1 win over Varvara Lepchenko.
Stosur took about two-thirds of the points when serving and more than half off Lepchenko's serve. She won 65 percent of the points overall in the second set.
No. 6-seed Jelena Jankovic was pushed to three sets by another young American in Mallory Burdette, eventually winning 4-6, 6-1, 6-4. Jankovic had nine aces but also eight double faults and she won a higher percentage (54-52) of points off Burdette's serve than when serving.
The U.S. crowd did see a local favorite advance, however, when Bethanie Mattek-Sands defeated Monica Puig 2-6, 6-1, 6-2. Mattek-Sands dropped her serve just once after the first set.
Also Monday, Francesca Schiavone survived a 3-hour marathon against Flavia Pennetta 7-6 (7-4), 6-7 (6-8), 6-4 in a match in which there were 19 breaks in 34 games. And Virginie Razzano ousted Svetlana Kuznetsova, who won this tournament in 2010, 6-2, 6-4
Celebrity Families of 2014 [PHOTOS]