Serena Williams' quest for a 24th grand slam singles title goes on after a fourth-round defeat by Elena Rybakina at the French Open.

Having come into the tournament with low expectations, Williams had looked solid through her first three matches, and, with big names falling by the wayside, the American surged up the list of title favourites.

She went into the match against her 21-year-old Kazakh opponent as the only top-20 player left in the bottom half but an unexpected finalist is now guaranteed after Williams fell to a 6-3 7-5 defeat.

Rybakina was not born when Williams made her debut at Roland Garros but a brilliant start to 2020 marked her out as a potential major challenger.

She has not shown the same form this season, and this was her first time through to the last 16 at a slam, but she played a calm and controlled match on the biggest stage of her life.

Rybakina's big serve and powerful forehand frequently proved too much for Williams, who did not play badly but lacked precision at important moments.

Rybakina moved ahead early, breaking to lead 3-1, and, although Williams responded with a break back for 3-4, she dropped serve again straight away and the young Kazakh clinched the set on her fourth chance.

The second set followed a similar pattern, with Williams staying in touch with Rybakina but vulnerable every time her opponent found her hitting zone.

A final break for 6-5 proved the key – Rybakina appearing nerveless as she converted her first match point.

Williams can at least take a good week of match practice into Wimbledon, which is surely her best chance of finally claiming that elusive 24th.

In the last eight, Rybakina will play her doubles partner Anastasia Pavlyuchenkova, who followed up her victory over third seed Aryna Sabalenka by knocking out Victoria Azarenka 5-7 6-3 6-2.

It will be Pavlyuchenkova's first quarter-final match in Paris since a run to the same stage a decade ago when she was 19.

"When I was actually playing the quarter-final, I was so emotional," she recalled. "I will never forget that match. I was 6-1 4-1 up against (Francesca) Schiavone. I was too young. I didn't know how to handle it.

"I think I'm more mature. I hope I show more maturity as well, smarter tennis, more consistent. I feel quite fit, as well. I'm also enjoying it much more than before. I know what I have to do, I know what I want to do. You're really in the present, so that's nice."

Azarenka used her post-match press conference to criticise the French Tennis Federation for a lack of equality. During the first week of the tournament, only one women's match was selected for what is supposed to be the marquee night session, even if it has felt anything but with fans absent.

Azarenka, who also voiced her frustration with the organisation of the tournament, said: "What concerns me is when somebody from the French federation is continually trying to say there is equality, and only pointing to prize money, which is true.

"Everything else, I wouldn't even agree a little with that. And that's disappointing."

Paula Badosa has reached her first Grand Slam quarter-final

The other quarter-final in the bottom half will pit Spain's Paula Badosa against Tamara Zidansek.

Zidansek, who beat Sorana Cirstea 7-6 (4) 6-1, is the first player representing Slovenia to reach the last eight at a slam.

"It means a lot to me that I'm able to get across the message to young people and everyone in Slovenia that we can do it," she said. "We're a small country, we don't have that many players, but we have good players."

Badosa's run is not as surprising given her excellent form on clay coming in and she defeated former finalist Marketa Vondrousova 6-4 3-6 6-2.