The American sent down a flurry of winners as she comfortably wrapped up the first set and recovered from a mini wobble in the second to seal victory in one hour and 16 minutes.
"She made me work for every point and it wasn't an easy win," said Williams.
"I think that was her goal today, was to put on a really good show and play really hard and show me what she's capable of. She's obviously capable of doing a lot on the court."
Round three results
4-Simona Halep (Romania) beat 15-Sabine Lisicki (Germany) 5-7 6-3 6-2
11-Ana Ivanovic (Serbia) beat Anastasia Pavlyuchenkova (Russia) 6-1 6-2
Caroline Garcia (France) beat 10-Sara Errani (Italy) 6-2 4-6 6-3
8-Maria Sharapova (Russia) beat Samantha Stosur (Australia) 6-4 6-3
3-Agnieszka Radwanska (Poland) beat Roberta Vinci (Italy) 6-1 6-1
1-Serena Williams (US) beat 14-Carla Suarez Navarro (Spain) 6-2 6-3
5-Petra Kvitova (Czech Republic) beat Lucie Safarova (Czech Republic) 6-4 6-3
2-Li Na (China) beat 16-Sloane Stephens (US) 2-6 6-3 6-2
- Sports & Recreation
- Maria Sharapova