Petersen looked set to push the former World No 1 going 3-1 up in the first set, but 10th-seeded Williams won five of the next six games.
The 37-year old finished the match with 28 winners and 22 unforced errors in comparison to Peterson's 8 winners and 20 unforced errors.
Williams was playing for the first time since withdrawing ahead of her third-round match in Miami because of a left knee injury.
Up next for Williams will be the victor of another blockbuster first round between Venus - who won the title in Rome back in 1999 - and Qatar Total Open champion Elise Mertens.
The make-up of Williams's new grass diet is unclear - one likely method of intake is through a smoothie drink - yet the effects were noticeable during her first match for nearly eight weeks.
"I did everything I could to stay fit and keep my cardio up. I knew that I love the clay season and I wanted to be a part of it".Читайте также: Huawei ready to sign 'no-spy' agreements
'When you're sedentary it becomes hard to manage your body so basically you have to just eat grass.
She broke twice more in the second and survived two break points against her while serving for the match, sealing victory after double-faulting on her first match point. But it worked and it paid off.
"Unfortunately, I felt really bad today out there on court and had a fever [of] 38.1 [degrees], so I couldn't continue the match". I feel like I'm taking it one day at a time. It seems like every tournament nowadays we meet early. "I was out much longer than I expected", Williams said.
Next up at the Italian Open: Sister Venus Williams in the siblings' first meeting on European clay in almost 17 years.
Wozniacki retired from her clash with Danielle Collins after losing the first set in a tie-break, a calf injury the issue on this occasion after back trouble prevented her from completing a match against Alize Cornet in Madrid last week.
Peterson, the world number 64, dug deep to grab two break points in the final game of the match but Williams saved both, before wrapping up the win in an hour and 15 minutes.
"Obviously it's about playing well at all the big moments, including this tournament".При любом использовании материалов сайта и дочерних проектов, гиперссылка на обязательна.
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