The sixth-seeded Spaniard broke serve in the 10th game of the first set and went up 3-0 in the second.
Magdalena Rybarikova of Slovakia ousted Russian wild-card entry Ksenia Pervak 7-5, 6-2. Also, Dominika Cibulkova struggled with her first serve and lost to Serbian qualifier Vesan Dolonc 3-6, 7-5, 6-3.
The 21st-ranked Cibulkova saved five break points in the 10th game of the second set before returning wide at 40-30 down on her next service game. The 92nd-ranked Dolonc broke the Slovak for a 4-2 lead in the third set and then saved a break point while serving for the match.
Volandri served for the match in the second set while leading 6-3, 5-4, but Lorenzi broke him and then won the next two games as well.
In an all-Italian second-round match, Lorenzi will face defending champion Andreas Seppi, who had a first-round bye.