Errani struggled for consistency in the opening set, committing a string of backhand errors to slip 4-2 down. However, the Italian fought back before eventually winning 7-6 (7/5), 6-2.
Errani will not find out her next opponent until Thursday but could face fifth seed Alexandra Dulgheru who beat Shuai Zhang 3-6 6-4 6-4.
Also triumphant on Wednesday was Errani’s compatriot, number two seed Roberta Vinci, after she eased past Timea Babos 6-2, 6-1 in one of the remaining first round matches. Vinci won nine uninterrupted games to help her wrap up victory in under an hour.
Fourth seed Julia Goerges was made to work considerably harder, eventually overcoming qualifier Daria Kasatkina, 7-6 (7/4), 6-4.
Polona Hercog is into the last eight after beating Patricia Maria Tig 6-0 6-2 while there were first-round wins for Sorana Cirstea and Teliana Pereira.