It has been a patchy season for the American, who won the Miami Masters in March, but followed that by exiting in the early rounds in Charleston.
Having taken a month out to rediscover her form she looked strong against Peng, ranked 42 in the world, winning eight of the first nine points to break serve.
Second round results
Anastasia Pavlyuchenkova (Russia) beat 6-Jelena Jankovic (Serbia) 6-2 5-7 7-6(3)
15-Sabine Lisicki (Germany) beat Irina Begu (Romania) 6-3 6-4
3-Agnieszka Radwanska (Poland) beat Svetlana Kuznetsova (Russia) 6-3 4-6 7-6(6)
Roberta Vinci (Italy) beat 13-Caroline Wozniacki (Denmark) 6-3 6-3
14-Carla Suarez Navarro (Spain) beat Alison Riske (U.S.) 6-2 6-4
1-Serena Williams (US) beat Peng Shuai (China) 6-2 6-3
4-Simona Halep (Romania) beat Lara Arruabarrena Vecino (Spain) 6-4 6-4
Caroline Garcia (France) beat Maria Kirilenko (Russia) walkover
- Sports & Recreation
- Carla Suarez Navarro