Roger Federer survived two match points to beat Borna Coric 2-6, 6-4, 7-6 and book his place in the Italian Open quarter-finals on Thursday after an exhausting day in Rome. Federer was forced to play two matches in one day after Wednesday's schedule was washed out due to rain. After beating Portugal's Joao Sousa 6-4, 6-3 in his second round clash in the afternoon, the Swiss third seed returned to the court hours later to face Croatia's Coric. It appeared as though the quick turnaround had done few favours for Federer, who quickly found himself trailing 4-0 on his way to losing the opening set. Coric had won two of his past three meetings with Federer and looked on course to extend his fine record against the world No 3, but the 37-year-old Swiss responded by levelling that match with a break of serve as Coric served at 4-5. Nothing could separate the two during the decisive third set and it was Coric who was in the driving seat during much of the tie-break, earning himself two match points at 6-4. However, Federer fought back to win five of the next six points to clinch victory. Also through to the men's quarter-finals is Spain's Fernando Verdasco, who followed up his shock win over fourth seed Dominic Thiem in his early match to beat Russia's Karen Khachanov 7-5, 3-6, 6-3. In the women's draw, Japan's Naomi Osaka won twice to reach the quarter-finals, retaining the world No 1 ranking ahead of the start of the French Open next week. She eased into the last eight in Rome with a 6-3, 6-3 win over Mihaela Buzarnescu. Osaka beat the 29th-ranked Romanian in 78 minutes after earlier beating Slovak Dominika Cibulkova by the same scoreline in one hour and 42 minutes in the second round, as players doubled up after the previous day was washed out. At the start of the day, the 21-year-old had needed to make the quarter-finals to ensure Romanian Simona Halep could not swipe the No 1 ranking and with it top seeding in the French Open. But Osaka's top spot was guaranteed when reigning Roland Garros champion Halep fell to Czech Marketa Vondrousova 2-6, 7-5, 6-3 in the second round. Osaka, who broke through by winning the US Open last year and Australian Open this year, did not survive the second round in her two previous appearances in Rome. Before this year Osaka had never made the last eight of any clay tournament, but has also reached the semi-finals in Stuttgart and quarter-finals in Madrid as she warms up for the French Open start on May 26. Osaka faces a moth-watering quarter-final clash with Madrid Open champion and world No 4 Kiki Bertens, who defeated Spain's Carla Suarez Navarro 4-6, 6-1, 6-3. Czech world No 7 Karolina Pliskova fought back from a set down to beat American Sofia Kenin 4-6, 6-4, 6-3 to set up a last-eight clash with Victoria Azarenka, who progressed from her battle of the former world No 1s after Garbine Muguruza retired injured midway through their match. Britain's Johanna Konta extended her fine form in Rome, following up on her win over French Open finalist Sloane Stephens by defeating Venus Williams 6-2, 6-4.