Venus, who won her only Rome title 20 years ago, defeated Elise Mertens 7-5, 3-6, 7-6 (4) after more than three hours, requiring nine match points before eliminating her Belgian opponent.
Serena had to withdraw from Miami prior to her third-round match, due to a knee injury.
As seen of late, Edmund was playing well enough to a certain point, but his confidence has descended to such a level that he lost 10 straight games from when the winning post came into sight. "We're just as fierce, Venus is just as fierce", Serena said.
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.
"It's been a while, I haven't played a ton of matches this year, not by choice, just by force".More news: Reynolds leads Rockies past Red Sox in 11th
"It felt good to finally be back out".
"I vaguely remember that, so I don't really remember", Serena laughed.
Next up at the Italian Open: Sister Venus Williams in the siblings' first meeting on European clay in almost 17 years. Hopefully I'll be able to keep it up. "I was out much longer than I expected", Serena said. "We'll both do the best that we can". 'It's been very bad. I've been working as hard as I could keeping up my cardio as much as I could with a knee injury'.
"I love the clay season and wanted to do everything to be a part of it and I'm here".
"I think the first match after a while, you're just trying to hang in there, just get the motor going". It will be the 31 time that they've played each other.More news: Watch the Super Mario Maker 2 Nintendo Direct here
Former world number four Dominika Cibulkova, won her match 6-2, 6-3 against Aliaksandra Sasnovich, and next meets US Open and Australian Open victor Naomi Osaka of Japan.
"But then I thought I did a pretty good job in the tiebreaker just staying ahead, being a little bit more comfortable and relaxed, being able to close it out once I finally got that last match point".
Spanish veteran Fernando Verdasco also had to come from behind to beat Kyle Edmund 4-6, 6-4, 6-2.
Other ladies advancing included Madison Keys, Garbine Muguruza, Johanna Konta, Annett Kontaveit, Victoria Azarenka, Lucky Loser Amanda Anisimova, Sofia Kenin, Viktoria Kuzmova, Dominika Cibulkova and Katerina Siniakova.More news: Serena Williams pulls out of Italian Open with knee injury