• Konta is first British woman in quarters since 1983 • ‘I’m hoping to go one or two more steps better’

Johanna Konta conquered her nerves and her opponent, Karolina Pliskova, in three compelling sets here on Sunday to become the first British woman to reach the quarter-finals of the US Open since Jo Durie 36 years ago.

“I’ve reached the fourth round for the first time and to go one step further is a massive achievement for me,” she said courtside after winning 6-7 (1), 6-3, 7-5. “I’m hoping to go one or two more steps better than that.”

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Konta is in the tougher half of the draw but, if she continues to hit the ball like she did in the first week and periodically in this up-and-down match, it is not beyond her to complete a quartet of grand slam semi-finals, having gone that far in Melbourne, Roland Garros and Wimbledon. After that? Then the proper dreaming can start.

“The key was just to keep going,” she said of a match in which she lost her way several times, hitting 45 winners alongside 36 unforced errors and benefiting from nine double faults by Pliskova, whose serve is her biggest weapon. “I knew there would be massive portions out there against Karolina when I didn’t know what I was doing. I’m just so happy.”

Konta entered the second week for the first time on the back of maybe her most consistent run in a grand slam tournament, her 92% hold of first serves second to Serena Williams’s 93%. When her serve clicks, she wins more often than not.

While Pliskova had the cushion of six wins from seven against Konta, they have split their two meetings on this surface. When she lost against Pliskova on the grass of her home town tournament in Eastbourne two years ago, Konta broke down in tearful frustration mid-match because she could not get her serve to do as she wanted. Coming into the fourth round for the third time, she had no such worries and was on song at the start.

In little over a quarter of an hour Konta was 3-1 up and she again had the support of the actor Tom Hiddleston in her team’s box courtside. Taylor Townsend, author of the feelgood comeback story of this US Open, has Kobe Bryant as her main cheerleader but Hiddleston is probably the biggest British star to lend glitter to the cause since Sean Connery was in Andy Murray’s box when he won here in 2012.

Celebrities aside, the tennis business on Louis Armstrong was entertainment enough for a capacity crowd basking in the sunshine. The third seed Pliskova was a pre-match favourite over the world No 16, and those odds were lengthening as Konta served for the first set – but she lost nine points in a row and had to force the tie-break, where both had a 7-7 log this season. Pliskova held her nerve to steal a set that had been in Konta’s firm grasp moments earlier.

At the start of the second Pliskova challenged an out call, which was overruled to hand her two break points, and Konta handed it to her with a wild forehand. A match that had started so promisingly for her had turned from a Sunday afternoon stroll into climbing the north face of the Eiger in flip flops.

Pliskova served a double-fault to return the favour but, just as Konta clutched at the lifeline, Pliskova broke her again. Konta was back on the Eiger, sliding backwards, as Pliskova struck the 10th of 16 aces to lead 3-1.

The contest took another twist when Pliskova dropped serve to give Konta parity in the sixth game, and the British player was energised for the first time in more than half an hour. She broke again and for the second time in the match the set was on her racket. This time she got the job done and took the match to a decider, where she brought an impressive 16-3 winning career record, compared to Pliskova’s 17-10.

Konta rediscovered her game during another dip in Pliskova’s level, holding from love-30 to stay on serve in the third. When Pliskova served her eighth double fault of the match in the fourth game, she followed it with her 14th ace in a quirky hold.

Nothing was certain from one shot to the next. After two hours and six minutes of see-sawing tennis Konta, behind in the cycle, served to stay in the tournament. She did so, to love, adding a third ace. Seven minutes later she was serving for the match after breaking Pliskova for the fifth time.

Konta, nor normally ruffled by off-court activity, complained to the chair when a whistle from the crowd mid-shot cost her a point at 3-3, then she hit long to hand Pliskova an unexpected break point. She saved with a cool, killer forehand, hit long on her first match point – and was relieved when her opponent replied in kind after two hours and 20 minutes.

Serena Williams took a tumble in the second set of her 6-3, 6-4 win over the world No 22, Petra Martic, but she finished strongly and will be ready for a quarter-final on Tuesday against China’s Wang Qiang.

Wang became the first Chinese player to get this far in the tournament since Peng Shuai lost to Caroline Wozniacki in her semi-final run five years ago. Wang was too good for Ashleigh Barty, beating the French Open champion 6-2, 6-4 in an hour and 22 minutes.