US Open 2015: Britain's Johanna Konta tries to keep cool at getting star billing against Petra Kvitova

Serena Williams, who is just three wins away from completing a calendar-year Grand Slam, will face her sister Venus in Monday’s quarter-finals

Johanna Konta has passed every test she has confronted here at this US Open, but on Monday the world No 97 faces a challenge of a different order. Having won three rounds in qualifying and beaten two top-20 players in Garbine Muguruza and Andrea Petkovic en route to the fourth round, the 24-year-old Briton now faces Petra Kvitova, the world No 4 and Wimbledon champion in 2011 and 2014.

Konta has even been given star billing on the Labor Day holiday ahead of Andy Murray, who will meet Kevin Anderson in the third match of the day in Louis Armstrong Stadium, the second of the show courts here. Konta and Kvitova will play the opening match of the night session in Arthur Ashe Stadium, which is a 24,000-capacity sell-out.

“I’m really looking forward to the challenge,” Konta said. “I have never played her. I have obviously seen her play. She’s a two-time Grand Slam champion. I’m feeling pretty lucky that I get an opportunity to play against such a player.”

Konta, who is only the second British woman (after Laura Robson three years ago) to reach the last 16 here since Jo Durie in 1991, used to have a reputation as a player who could struggle to handle big-pressure moments. However, her transformation this year has been remarkable.

In her second-round marathon, which at three hours and 23 minutes was the longest women’s match here for 45 years, Konta looked mentally stronger than Muguruza. In Saturday’s third round she held on against Petkovic despite the German’s late fightback. Petkovic, who had been suffering with a cold, took a medical time-out in the second set but recovered to save five match points before going down 7-6, 6-3.

Konta, who has been consulting a mental coach since the end of last year, admitted: “This is no secret. I’m not the calmest or the most really cool person out there. Everyone knows that I can be quite bubbly and emotional. It’s always been a work in progress for me to keep things the way I want to keep them.”

She added: “It would be silly to say I wasn’t nervous or wasn’t feeling tension. I didn’t feel all of it was my own tension. I felt like it was a lot of tension around me. I kept on consciously reminding myself how lucky I am to be in this position: win or lose, that I get to experience this whole thing that was happening out there. I just feel very blessed.”

Saturday’s victory was Konta’s 16th in a row following her two title triumphs on the International Tennis Federation circuit this summer. It also ensured that she would climb next week to a career-high position in the world’s top 60, just behind Heather Watson, the British No 1. She has already guaranteed herself prize money of $213,575 (about £141,000).

Kvitova, meanwhile, has had a difficult year after missing two months with what was later diagnosed as glandular fever. She had not won a match on the north American hard-court circuit until she took the title in New Haven before arriving here.

Serena Williams, who is just three wins away from completing a calendar-year Grand Slam, will face her sister Venus in Monday’s quarter-finals. Both won their fourth-round matches in convincing fashion. Venus, who reached the final on her debut 18 years ago, beat Estonia’s Anett Kontaveit 6-2, 6-1 in just 50 minutes, while Serena beat her fellow American, Madison Keys, 6-3, 6-3. The big-serving Keys matched the world No 1 until she was broken at 3-4 in the first set after two successive double faults.

Eugenie Bouchard, who suffered a fall in the locker room after her third-round victory, pulled out of the tournament last night with concussion just hours before she was due to play Roberta Vinci.