The eight-time Rome champion Nadal cruised previous Jeremy Chardy, 6-0, 6-1, and can subsequent meet Nikoloz Basilashvili, whereas Djokovic eradicated Denis Shapovalov, 6-1, 6-3, and can play both Philipp Kohlschreiber or Marco Cecchinato.
Shapovalov appeared distracted by a flyover from fighter jets performing an air present and double-faulted at hand Djokovic a 3-1 lead within the first, prompting the 20-year-old Canadian to have a phrase with the chair umpire.
Additionally, the Spanish veteran Fernando Verdasco rallied previous fifth-seeded Dominic Thiem, 4-6, 6-4, 7-5.
The highest-ranked Osaka comfortably beat Dominika Cibulkova, 6-3, 6-3, and can subsequent face Mihaela Buzarnescu.
Osaka, who can maintain onto the No. 1 rating by reaching the quarterfinals, hit 44 winners and 12 aces.
“My serve was actually good,” Osaka stated. “I simply tried to be actually calm.”
The Czech teenager Marketa Vondrousova rallied previous second-ranked Simona Halep, 2-6, 7-5, 6-3, for her second win over the Romanian this 12 months.
Halep, who was a finalist in Rome the final two years and is making ready to defend her French Open title, took a medical timeout early within the third set and acquired therapy on her left leg.
Others advancing included Stefanos Tsitsipas, Kei Nishikori, Diego Schwartzman and Jan-Lennard Struff, and Kiki Bertens, Petra Kvitova, Garbiñe Muguruza, Johanna Konta and Kristina Mladenovic.