Errani committed a string of backhand errors in the second round match to trail 4-2, before the Italian made a comeback against her Israeli opponent.
Polona Hercog of Slovenia also advanced to the quarterfinals, defeating Patricia Maria Tig of Romania 6-0, 6-2.
Errani's compatriot Roberta Vinci, seeded second, eased past Hungary's Timea Babos 6-2, 6-1 in under an hour to make it to the second round.
In other first round matches, No. 4 Julia Goerges of Germany overcame qualifier Daria Kasatkina of Russia, 7-6 (4), 6-4 and Sorana Cirstea of Romania beat Sesil Karatantcheva of Bulgaria 6-2, 6-2.