Twenty-four hours after two more of the top women’s seeds shivered and slid out of the French Open, Serena Williams booked her place in the quarter-finals with a performance of calm authority. On another cold and dank morning here at Roland Garros, the world No 1 needed just 62 minutes to beat Ukraine’s Elina Svitolina 6-1, 6-1.

At least it was not raining, which must have come as a huge relief to tournament organisers after the previous two days. Monday was a complete wash-out, while only two hours of play had been possible on Tuesday, though that was time enough for Agnieszka Radwanska and Simona Halep, No 2 and No 6 in the world respectively, to go out of the tournament, complaining bitterly about having to play in the cold and the wet.

Williams and Svitolina had been on the schedule to play on both Monday and Tuesday and when they finally got on court the world No 1 wasted no time getting down to business. She won the first four games without reply and played the big points well throughout. Svitolina had eight break points but converted only one of them, whereas Williams took six of her eight opportunities.

“It was not my day today,” Svitolina, the world No 20, said afterwards. “She was playing great. I think she was serving well at the right moment and really moving the ball around the court, which for me was a little bit unexpected.”

Williams sympathised with those who had had to play in such difficult conditions the previous day. “I'm sure it was really tricky and must have been really difficult to keep warming up and keep going, going, going,” she said. “I was really fortunate to get my match in and out today, so that worked out well.”

The American now faces the world No 60, Kazakhstan’s Yulia Putintseva, who is through to the quarter-finals of a Grand Slam event for the first time thanks to a 7-5, 7-5 victory over Spain’s Carla Suarez Navarro. At the age of 21, Putintseva is the youngest player left in the competition.

Venus Williams will not be joining her sister in the quarter-finals after going down to Timea Bacsinszky, who beat the veteran American 6-2, 6-4. Bacsinszky, a semi-finalist here last year, will now meet the Dutchwoman Kiki Bertens, who beat Madison Keys 7-6, 6-3 Bertens, the world No 58, is through to the quarter-finals of a Grand Slam tournament for the first time in her career.

The semi-final line-up in the other half of the draw was decided when Australia’s Sam Stosur and Spain’s Garbine Muguruza ended the hopes of surprise quarter-finalists. Stosur beat the world No 102, Tsvetana Pironkova, 6-4, 7-6 while Muguruza ended the run of the world No 108, Shelby Rogers, winning 7-5, 6-3.