The American top seed did not have it all her own way from the outset, and found herself 0-40 down on serve in the opening game following two double faults.
However, she quickly got into her rhythm and - after saving all seven of her Italian opponent's break-point opportunities - posted a 6-1 6-1 victory in one hour 17 minutes.
"It was a little frustrating because I felt like I should be putting the balls away more quickly, but she was so quick and was running every ball down," the 15-time major winner said on www.wtatennis.com.
"I was trying to get myself more pumped up and more energetic out there, because I believe she was ranked in the top 10 at one point.
"I think I was off, footwork-wise, but it's always good to win a match and then just keep going."
The 31-year-old will face Ayumi Morita in round three after the Japanese saw off 31st-seeded Belgian Yanina Wickmayer 7-6 (7/2) 2-6 6-3.
Serena's sister Venus also progressed, albeit having been pushed to three sets by Japanese veteran Kimiko Date Krumm. The 19th-seeded American triumphed 7-6 (7/3) 3-6 6-4 to set up a third-round clash with compatriot Sloane Stephens, the 16th seed battling back from a first-set wobble to sink Belarus' Olga Govortsova 0-6 6-4 6-4.
World number four Agnieszka Radwanska opened her title defence with a comfortable 6-3 6-2 win over Hsieh Su-wei.
The Pole, a winner in Auckland and Sydney this year, broke her Taiwanese opponent four times in a match which lasted 65 minutes.
China's fifth seed Li Na made a successful return from a seven-week injury absence with a 6-3 6-1 victory over Holland's Kiki Bertens.
Seventh seed Petra Kvitova and ninth seed Caroline Wozniacki each needed three sets to advance, the Czech sinking China's Shuai Peng 5-7 6-2 6-2 and the Dane overcoming Czech Republic's Karolina Pliskova 5-7 6-3 6-3.
Thirteenth seed Dominika Cibulkova, Varvara Lepchenko (25) and Kirsten Flipkens (30) enjoyed much more straightforward passages with respective straight-sets wins over Kristina Mladenovic, Irina-Camelia Begu and Stefanie Voegele.
Marion Bartoli was the highest-seeded casualty, retiring with a foot injury against Andrea Petkovic. The German led 6-3 4-1 when the Frenchwoman called it a day.
Other seeds to fall at the second-round stage were Lucie Safarova (17), Anastasia Pavlyuchenkova (23), Julia Goerges (24) and (27), who were despatched by Romina Oprandi, Garbine Muguruza, Ajla Tomljanovic and Magdalena Rybarikova.