The first round wrapped up early Wednesday, with 2012 junior champion Annika Beck among the winners.
Fellow teenager Ashleigh Barty beat Lucie Hradecka for her first Grand Slam main draw match win.
No.29 seed Varvara Lepchenko hit 23 forehand winners to beat Elina Svitolina second round, 76(5) 61.
Elsewhere, No.8 seed Angelique Kerber had no trouble with Jana Cepelova in her second round, 62 62.
And No.5 seed Sara Errani absolutely cruised past feisty teenager Yulia Putintseva in two, 61 61.
Errani's best friend and doubles partner No.15 seed Roberta Vinci beat Galina Voskoboeva, 64 46 62.
No.20 seed Carla Suárez Navarro rallied from 63 20 down to make it past Shelby Rogers, 36 64 64.
No.14 seed Ana Ivanovic had no issues in her match though, sweeping aside Mathilde Johansson, 62 62.
No.10 seed Caroline Wozniacki did have trouble though, falling to Bojana Jovanovski, 76(2) 63.
No.19 seed Anastasia Pavlyuchenkova followed Wozniacki to the sidelines, falling to Petra Cetkovska.
Cetkovska beat Pavlyuchenkova, 75 26 64. She is playing her first event of 2013 following injury.
Heather Watson's comeback from illness was cut short though - she fell to Stefanie Voegele in three.
Serena Williams, ranked and seeded No.1, blitzed Caroline Garcia, 61 62, her 26th straight win.
Virginie Razzano beat Zuzana Kucova to reach the third round - and put an end to Kucova's career.
And at night, Monica Puig rallied from 4-2 down in the second set to defeat Madison Keys, 64 76(2).