Johanna Konta soared, dipped and soared again to defeat Lauren Davis in three sets on her way to reaching the third round of the French Open, where she might have expected to meet the world No 4, Kiki Bertens, for the second time in a fortnight, but instead will play the young Slovak Viktoria Kuzmova for the first time.

Davis, heavily strapped above and below her left knee, gave Konta a stern argument mid-match and in the third set before the British No 1 won 6-3, 1-6, 6-3 in the Bullring, the perfect setting for such a tough struggle.

French Open 2019: Konta wins, Federer and Nadal ease through – as it happened Read more

Konta broke through after 44 minutes and served out the first set through deuce – just as news came through that Bertens, whom she defeated in the Rome semi-finals, had retired when 3-1 down against Kuzmova, ranked 46 in the world.

“I was sick before the match and am really aching,” the Dutch fourth seed told the tournament doctor before walking off court. “There’s nothing in my arms, nothing in my legs. I’m shaking like hell.”

Konta shook too, for different reasons. She collapsed in the second set before resetting in the decider, and again made hard work of it. Davis surrendered an early break with an overcooked drive volley, saved two match points on her own serve to avoid the bagel then broke back for 2-5 after two hours of an enthralling contest.

When Konta, serving for the match at 5-3, served a double-fault to hand the American three break points, it seemed nerves would consume her, but a brave drop-shot got her back into it. Davis hit long at deuce. Konta blew a third match point with a similarly hot reply, but steadied herself to smash away the fourth chance.

Having not won a main draw match here in four previous visits, Konta has a wonderful chance to go deep in the tournament. She said: “I’m very pleased. There wasn’t so much that I did wrong. I had a good run to get to 5-0, but I knew with Lauren it was never over until we shook hands. More than anything, I feel I handled it well. It was a very tricky match. I feel very grateful for how much support I had.”

In the same quarter of the draw Garbiñe Muguruza, who has struggled lately, looked happy enough with a 6-4, 6-1 win against Johanna Larsson, but will have a tougher time of it against the ninth seed, Elina Svitolina, who went through to the third round when Kateryna Kozlova withdrew injured – and who has won six of their seven matches.

Still, the Spaniard, whose pedigree is undoubted but her resolve less so, is looking forward to the challenge. “These are the type of matches that I want to play,” she said. “It could be any deep-round match, but it’s in the third round. Maybe it’s a bit too early, but too bad. It will be very interesting. In the women’s game, it’s tough. If you don’t play well you go home very fast. So, you’ve got to be competitive and, on top of that, play your A game all the time.”

The prize is a fourth-round match against either Sloane Stephens, who had to grind towards the end of her 6-1, 7-6 (7) win against another Spaniard, Sara Sorribes Tormo, or the Slovak Polona Hercog, who took two and a quarter hours to defeat the American Jennifer Brady, 6-3, 5-7 (8), 6-4. Of that foursome, Svitolina is clearly best placed to advance in a quarter of the draw with plenty of quality – and minus Bertens.

In the bottom half on that side of the draw, the world No 2, Karolina Pliskova, took less than an hour to put a 6-2, 6-2 score on the Slovakian qualifier Kristina Kucova, who had eliminated the former champion Svetlana Kuznetsova in the first round. The Czech next plays the 31st seed, Pera Martic, whose 6-1, 6-1 win against Kristina Mladenovic looked almost as easy.

Also through to the third round are Kaia Kanepi against Veronica Kudermetova, the 12th seed, Anastasija Sevastova, against the world No 20, Elise Mertens, and Carla Suáez‑Navarro (28) who plays Marketa Vondrousova, who beat Angelique Kerber’s conqueror, Anastasia Potapova in two quick sets.