Venus Williams will take on her sister Serena in the second round of the Italian Open after battling past Elise Mertens 7-5, 3-6, 7-6 (7/4) in Rome on Monday.
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.
Serena finished with 28 winners to Peterson's eight, and committed only two more unforced errors than the 58th-ranked Swede, 22-20.
Williams was back in action in only her fourth tournament of the season and the first since being forced to withdraw from the Miami Open in March due to a 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.More news: Kremlin Says Concerned over Escalating Iran Tensions despite Pompeo Claims
Serena Williams will likely face her sister, Venus Williams, provided the latter wins her match against Elsie Mertens. Serena holds an 18-12 lead and she won the most recent meeting when she defeated Venus in the third round of the 2018 U.S. Open.
"I didn't get to train too much".
She next plays either Denmark's Caroline Wozniacki, the 11th seed, or American Danielle Collins, for a place in the third round. This is her only preparatory tournament for the French Open and early last week she was seen in a stunning yellow dress attending the Met Gala in NY.
"It was a very long match", Venus said during her press conference.
"It's really fun because I took her to the Colosseum, then I took her to the (Trevi) fountain", she said. "I did everything I could to stay fit and keep my cardio up".More news: Xiaomi launches Mi Express Kiosk: A smartphone vending machine in India
"It was really cool to share my favourite city with her, some of my favourite things to see".
"I love the clay season and wanted to do everything to be a part of it and I'm here".
Also progressing was Croatia's Borna Ćorić after he beat Canada's Felix Auger Aliassime 6-7, 6-3, 6-4.
Others advancing on the women's side included Madison Keys, Garbine Muguruza, Johanna Konta and Dominika Cibulkova.
Among other matches, Great Britain's Johanna Konta was a 6-4, 6-1 victor over Alison Riske; Spain's Garbine Muguruza beat China's Saisai Zheng 6-3, 6-4, and Victoria Azarenka of Belarus knocked off China's Shuai Zhang 6-2 6-1.More news: NY continues to lead the nation in measles outbreaks
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