The fourth-seeded Medina Garrigues was upended Italy's Maria Elena Camerin 6-1, 6-3 on the clay courts of the Country Time Club.
The Spaniard, who was the defending champ after beating Slovenian Polona Hercog in last year's Palermo final, also won the event in 2001 and from 2004-06.
Errani, meanwhile, dispatched Romanian Edina Gallovits-Hall 6-1, 6-1 to move on, and second-seeded Italian Roberta Vinci doused countrywoman Karin Knapp 6-2, 6-2.
Also Tuesday, No. 3 seed Julia Goerges of Germany ousted Uzbekistan's Akgul Amanmuradova 6-4, 7-6 (10-8) and fifth-seeded Spaniard Carla Suarez Navarro handled New Zealand's Sacha Jones 6-4, 6-1.
Other Day 2 winners included American Julia Cohen, Anna Tatishvili of Georgia, Britain's Laura Robson, Estrella Cabeza Candela of Spain and Austrian Patricia Mayr-Achleitner.