It remains to be seen whether Serena Williams can play herself into form over the coming days and rise to become a true contender for the French Open title but her effort alone cannot be faulted. The three-times Roland Garros champion moved into the third round by punctuating an arduous three-setter with a strong finish, beating Mihaela Buzarnescu 6-3, 5-7, 6-1 to advance. The victory, only her third of the clay season, may not have been convincing but during this uncertain period every victory marks a small step forward. After looking sublime in Australia, beating two top-10 players before losing in the semi-finals to the eventual champion, Naomi Osaka, she spent three months away and her absence has shown. So Williams is in Paris with expectations about as low as they have ever been for her at a major. Rather than mental, the question here is simply whether she can elevate her level enough. Williams is an underrated clay player – she has won three titles in Paris – but for her game truly to suit the slow, high-bouncing surface she has to be in top physical shape. For a while it seemed Williams could have a comfortable afternoon. She opened the match serving well, easily navigating her early service games. By the end of the set her uncertain forehand obliged as she dismantled Buzarnescu’s serve; and she conceded only three points on her own serve in the opening set. Buzarnescu is a tidy, diminutive lefty who generates power and depth through her feathery timing. She was a top-20 player in 2018 but her upwards trajectory was halted by injuries and she is now ranked 174. As the match went on and she began to read Williams’ serve, she grew more comfortable and began to show her ball-striking ability. So often it was Buzarnescu bossing the rallies, with Williams forced into uncomfortable positions. She ended the set with a lovely running backhand crosscourt winner. Williams responded to the second set correctly, tightening her serve and reducing her unforced error count. Her movement also improved with more time on court, underlined when she somehow pulled out a 19-stroke rally at 2-0 that included an overhead, a defensive lob from Buzarnescu and an exhausted dropshot from Williams before the American flicked a passing winner . Both women laughed, with Williams apologising as Buzarnescu applauded. The tension broke and Williams never looked back. Unlike in Australia, where Williams had to go through three of the current top five to reach the final, her half of the draw is not a bad place to be. It has already seen the sad withdrawal of Naomi Osaka, a freak injury suffered by Petra Kvitova and an early loss for Bianca Andreescu, meaning Williams is the second highest ranked player left in her half behind the third seed, Aryna Sabalenka. They could face each other in the quarter-finals. First she faces Danielle Collins, playing her first tournament since undergoing surgery to address complications from endometriosis, a condition where tissue similar to the lining of the womb grows in different parts of the body. “I think, as most women in the world who have our menstrual cycles, sometimes when we’re dealing with these painful moments, we learn to accept it,” she said this week. “And for me things started to become too abnormal and really unhealthy. It certainly presented its challenges but it’s been really kind of shocking, like since surgery I’ve just felt so much better, especially with my back pain.” Earlier Japan’s Kei Nishikori bolstered his reputation as the greatest fifth-set player of the 21st century by beating the 23rd seed Karen Khachanov 4-6, 6-2, 2-6, 6-4, 6-4, his second five-set match in the first two rounds. Nishikori’s record in the major deciders is now 26-7 (79%), sixth on the all-time list. Importantly the Tokyo Olympics entry list will be formed from the rankings at the end of Roland Garros. After missing nearly a year with an elbow injury, there was a chance that Nishikori may not have qualified for his home Olympics. Today’s win places his live ranking around 62nd and within the entry-list cut-off. In the evening session, world No 2 Daniil Medvedev fought back to beat Tommy Paul 3-6, 6-1, 6-4, 6-3 and reach the third round. The Russian had never won a singles match in Paris before this year, but rallied impressively after dropping the opening set. Alexander Zverev and Stefanos Tsitsipas both progressed in straight sets, defeating Roman Safiullin and Pedro Martínez respectively. Organisers have announced that a men’s doubles pairing have withdrawn from the tournament after testing positive for Covid-19. The pair were not named but Croatian top seeds Mate Pavic and Nikola Mektic have been replaced in the draw by Martinez and Pablo Andújar. Pavic and Mektic’s expected opponents, Feliciano López and Jaume Munar, have also been removed with alternates yet to be named.