The Italian is just one of two top six-seeded players left in the Tier III tournament. Top seed Flavia Pennetta of Italy, third-seeded Frenchwoman Alize Cornet and fourth seed Emilie Loit all suffered first-round losses.
Third seed Pauline Parmentier of France will meet Colombian Catalina Castano on Thursday.
By virtue of her win, Errani will face Spanish qualifier Nuria Llagostera Vives, who downed Rossana de los Rios of Paraguay 6-2 6-0, for a place in the last four.
Local favourite Mariana Duque Marino thrilled the home crowd with a surprisingly easy 6-1 6-2 win over fifth seed seed Yvonne Meusburger of Austria in Thursday's final match.
The victory sets up a quarter-final match with Argentina's Ma. Emilia Selerni.