Errani, seeded third in the tournament, defeated Karin Knapp 6-4, 6-3. She won five of the nine break chances she had and took nearly half (30-of-61) of the points off Knapp's serve.
Errani did lose her serve twice but still won about 60 percent of the points on serve.
No. 8-seeded Kirsten Flipkens was on the court less than an hour in a 6-1, 6-3 romp past Yvonne Meusburger. Flipkens dropped just 12 points over eight games serving and didn't face a break point.
Elina Svitolina also posted a lopsided win, beating Galina Voskoboeva 6-1, 6-2, and Andrea Petkovic ousted Kristina Mladenovic 6-4, 6-2 with six breaks in nine receiving games.
Alize Cornet played for almost 3 hours before gaining a spot in the quarterfinals with a 6-2, 6-7 (2-7), 6-3 win over Barbora Zahlavova Strycova, who was a substitute for second-seeded Petra Kvitova. Kvitova withdrew from the tournament due to a respiratory problem.
Friday's quarterfinals have top-seeded Maria Sharapova taking on Flipkens while fourth-seeded Angelique Kerber plays Anastasia Pavlyuchenkova. The other quarterfinals have Errani playing Svitolina and Petkovic going against Cornet.