Reigning Internazionali d'Italia champion Elina Svitolina eased into the last 16 on Tuesday, while Maria Sharapova reached the second round.
Svitolina defeated Simona Halep in the 2017 final and the Ukrainian was the first name into the third round after a straight-sets win over Petra Martic.
Sharapova, a three-time winner of the WTA Premier 5 event, did not enjoy such a straightforward passage but the Russian eventually prevailed after being taken the distance by Ashleigh Barty.
Svitolina was joined in the last 16 by fifth seed Jelena Ostapenko, who made light work of seeing off Zhang Shuai 6-2 7-5, while Angelique Kerber made a successful return from injury in defeating Zarina Diyas.
ONE CHAMPION MEETS ANOTHER
Before taking on Martic, Svitolina spent time with Roma icon Francesco Totti over the weekend, prior to the Giallorossi's meeting with Juventus.
Svitolina was treated to a tour of the Stadio Olimpico, while she was presented with a club shirt bearing her name and the number 10 famously worn by former Serie A champion and World Cup winner Totti.
Although Roma could not halt Juve's charge to a seventh straight title on Sunday, Svitolina had more success two days later in ousting Martic 6-1 6-2, a display which included 24 winners and just nine unforced errors.
CAREFREE SHARAPOVA OVERCOMES RAIN DELAY
Sharapova kept her cool at the end of a lengthy rain stoppage and a gruelling two and a half hours on court against Barty, coming through 7-5 3-6 6-2 against the 16th seed to set up a meeting with Dominika Cibulkova.
"This tournament has been special in my career, and brought me some great matches," said Sharapova, champion in 2011, 2012, and 2015. "I'm a little bit more relieved this year...and just playing, and not worrying about anything else, which is nice.
"The beauty of what we do is you don't know until you go out and you play. Sometimes, you feel your best and you play great and you come out losing the match, and sometimes you don't play so well and you come out winning the match."
KERBER PLAYING WITHOUT PAIN
A thigh injury had seen Kerber retire from the Stuttgart Open last month, but the German returned to Tour action with a 6-2 7-6 (8-6) victory over lucky loser Diyas.
"I'm actually happy after the last two weeks that I'm back," Kerber said. "After Stuttgart it was a really tough time because I had a lot of pain in my leg, and now I can say I was without pain the whole match and I could play my game like I practiced the past few days.
"It was a bit up-and-down match, but at the end, I think the whole match was a good match from me. Especially because it's the first round, the first match on clay outside, it's always a little bit different and tricky, but I think the whole thing was a good day."