The sixth-seeded Spaniard broke serve in the 10th game of the first set and went 3-0 up in the second. Dushevina entered the main draw as a lucky loser.
Magdalena Rybarikova of Slovakia ousted Russian wild-card entry Ksenia Pervak 7-5, 6-2.
Volandri served for the match in the second set while leading 6-3, 5-4, but Lorenzi broke him and then won three consecutive games.
In an all-Italian second-round match, Lorenzi will face defending champion Andreas Seppi, who had a first-round bye.