Anderson had 11 aces and did not drop serve against the 34th-ranked Italian.
After reaching a career-best ranking of No. 10 in 2015, Anderson fell to No. 80 in January after a persistent run of injuries.
Victories in the past month over Richard Gasquet and David Ferrer lifted the 31-year-old South African to No. 62 ahead of a final warm-up for the French Open.
Also, sixth-seeded Sam Querrey beat Daniel Altmaier of Germany 6-3, 6-4.