Johanna Konta has always believed in herself. After her quite superb victory over the American Sloane Stephens on day 10 of the French Open, so do most of her critics, along with a growing army of fans and former players – including the best clay-courter in the history of women’s tennis, Chris Evert.

It was not just the result – a 71-minute 6-1, 6-4 drubbing of the 2018 finalist and US Open champion of a year earlier to reach the semi-finals – but the ruthless performance, which followed a similarly excellent win in the fourth round on Sunday, when the British No 1 thrashed her friend Donna Vekic in two sets. Before that, there were a string of wins from Rabat to Rome, as she clambered back up the WTA rankings from a low of 47 at the start of the clay season, arriving in the French capital seeded 26th, and convinced she could wipe away the memory of four successive first-round defeats.

French Open quarter-finals: Konta blitzes Stephens in straight sets – live! Read more

It was that depressing sequence that made people wonder if she had what it takes to leave her impression on the red dirt of Roland Garros. Now she is in a good place to replicate the deeds of Sue Barker in the 70s and Jo Durie in the 80s, the last British women to go this deep in Paris.

But Konta is not making her charge at the title for them, as she has made clear, politely but firmly. She is doing it for herself – and quite possibly her dog, Bono, whom she adores and who will no doubt be sitting at the feet of her parents watching on TV back in Eastbourne when she walks on to court on Thursday to face Marketa Vondrousova, the exciting young Czech, who beat the 31st seed, Petra Martic, 7-6 (1), 7-5 in fast- fading light on Court Suzanne Lenglen.

Evert, who had predicted that her US compatriot would win the quarter-final, perhaps easily, led the accolades on Tuesday . The seven-times French Open champion, whose winning record on clay of 94.55% is the best in her sport’s history, conceded afterwards: “Playing like this, there isn’t anyone who could beat her. That was one of the best clay-court matches ever. I could not see this coming. I’m speechless. Not even giving her a glimpse … Jo Konta, I take my hat off to you.”

Konta has already matched Durie’s feat of getting to the semi-final in 1983, and is now following Barker’s achievements in more ways than one. Barker, known to the current generation for her TV appearances on the BBC as much as her tennis, is the last British woman to win here, and it is an indictment of the game, perhaps, that her triumph over Renata Tomanova in the final was 43 years ago. She also made semi-finals at Wimbledon and Melbourne and reached the fourth round at the US Open – which Konta has done.

Now she has the challenge of going two steps further to rank alongside Barker. If she wins the whole show she will return to the top 10 for the first time since 2017, her golden summer, and she will go to Wimbledon, via Eastbourne, with renewed ambitions of winning again.

It might all fall to pieces, of course, but she showed in her dominance of Stephens, who had recovered from a slow start to eliminate the 2016 champion Garbiñe Muguruza on Sunday, that she deserves to compete and win in this company.

“There is not much you can do when someone is playing like that,” Stephens said of Konta. “She definitely played her game today. I didn’t get a chance to get into the match, but sometimes that happens.” And always for a reason. The reason this time was all on Konta’s racket.

Facebook Twitter Pinterest Konta in action during her quarter-final against Sloane Stephens. Photograph: Kai Pfaffenbach/Reuters

The only sign of nerves from her was in the first game, when she saved a break point and held through deuce. From there to the end, she bossed nearly every exchange. The first set flew by in 25 minutes. Konta pushed on relentlessly, giving her opponent no chance to get back into the fight.

She surrendered just one point on her serve in the second set – with a double fault. That was the difference between them, along with Konta’s power hitting on both wings.

The American might have thought she was playing herself, so pinpoint direct were the replies across the net. Particularly memorable was a backhand return into the deuce corner that left Stephens gobsmacked and rooted to the clay.

This was as good as Konta can play, and a deal better than Stephens was managing in response. If Konta had found her best tennis to beat Vekic in the fourth round, this was a notch up. Her challenge was to sustain a level that must have surprised even her – and probably her low-key coach, Dimitri Zavialoff.

There was no hiding place for Stephens in the second set, as Konta broke her for the third time. Down a set and 1-3 with ball in hand, the American looked distinctly uninterested until she found a couple of huge forehands and a good serve to hold to love. But she went to the service line after just over an hour needing to hold to stay in the tournament, and she just about hung on. Her final forehand slid into the tramlines – and only then did Konta’s face reveal her true joy.