Simona Halep and Karolina Pliskova cruised into the last eight at the Internazionali d'Italia on Friday, while Garbine Muguruza impressed again.
Tournament favourite Halep eventually looked comfortable in her 7-5 6-4 against Dayana Yastremska, but the Romanian had to fight back from a break down in the opening set as she was put on the back foot.
Halep slid 3-0 down in the opener, but she produced an admirable response when winning 12 of the following 13 points as she levelled up.
Another break from 5-5 allowed Halep to take charge, and from there she rarely looked in trouble, remaining in the ascendancy early in the second as she went 3-0 up, ultimately seeing out the win professionally despite Yastremska giving herself a chance with a break of her own.
"It was not easy against her because you don't really have the rhythm. She hits it very strong and it's tough to return her balls," Halep said, highlighting the need to get her head straight after the early wobble.
"After I lost the first three games, I just had to focus a little bit better and stop giving her the balls that she likes.
"I tried to change it up a little bit, make her move, [hit shots] a little bit high. I think during the match I found some solutions that were good to win.
"Big picture, I think it was a great match and gives me confidence that even in these conditions with a big hitter that I could win in two sets."
Awaiting Halep is a meeting with Yulia Putintseva, who fought back from a set down against fellow Russia-born Kazakh Elena Rybakina to edge an absorbing contest 4-6 7-6 (7-3) 6-2.
Second seed and defending champion Pliskova came through fairly comfortably against Anna Blinkova 6-4 6-3, with the Czech next going up against Elise Mertens, who saw off Danka Kovinic in similarly routine fashion with a 6-4 6-4 victory.
Another tantalising quarter-final will be contested between Victoria Azarenka and Garbine Muguruza. Spaniard Muguruza caught the eye as she beat seventh seed Johanna Konta 6-4 6-1, not dropping serve once against her British opponent.
Azarenka, who incredibly crushed Australian Open champion Sofia Kenin without dropping a game on Thursday, should be fresh for the quarter-final as her last-16 opponent Daria Kasatkina retired due to an ankle injury at 6-6 in the first set of their contest.