Venus Williams not only plays a fellow American in the semi-finals of the 2017 US Open; she plays a fellow African American, Sloane Stephens, and, in a time of simmering racial tension across the country, the significance is not lost on either of them.

Stephens, after a heart-stopping win over the Latvian Anistasija Sevastova on the ninth afternoon of the tournament, said of sharing quarter-final status with Williams, Madison Keys and Coco Vandeweghe, “It’s great for American tennis. It’s great for African-American women. I hope that we keep it going.”

She added, “Venus is our leader. She’s who everyone looks up to. She’s a great player, a great person, a great leader. There is not anything bad you can say about Venus. I’m honoured to be able to play at the same time as her. I’m happy she’s still playing. She means a lot to the game.”

Sloane Stephens beats Anastasija Sevastova to make US Open semi-finals Read more

The last time four American women contested the semis of a slam was at Wimbledon in 1985: Martina Navritolova, the eventual champion, the runner-up Chris Evert, Kathy Rinaldi and Zina Garrison.

And now, having seen off the impossibly artful Sevastova 6-3, 3-6, 7-6 (4) in two hours and 28 minutes on a frenzied Arthur Ashe court with the roof open, Stephens must get ruthless against Williams, who later beat Kvitova 6-3, 3-6, 7-5 (2) in two hours and 34 minutes under cover on the same court.

They have cut contrasting paths on the same journey. Williams, ninth in the world and two wins away from the No2 spot, is riding the adrenalin of experience and proven pedigree, while 24-year-old Stephens, unseeded and back in the game after 11 months out with injury, is grabbing at the fumes of outrageous optimism.

For the second night in a row, the crowd played a significant part in the result. On Monday, Juan Martin del Potro admitted he was ready to quit after going two sets down against Dominic Thiem, before he rallied to prevail over five sets with the encouragement of the fans.

After going 1-3 down in each set before pulling it out in the tie-break, Williams told the fans in her courtside interview, “I felt every single one of you guys behind me, all 23,000. That feels good. I didn’t want to let you guys down.”

Williams paid tribute to her beaten foe too. Having survived her own off-court trauma when cut down by the energy-sapping Sjogren’s Syndrome in 2011, she was aware of the strength of mind it took for Kvitova to recover from a knife attack in her home last December.

“Everything she’s gone through, is unbelievable,” she said. “It’s so wonderful to see her back and playing amazing tennis. I was excited to be able to play her, to go down to the wire. I hope we have more matches like that.”

It was the most curious struggle. Both made and squandered so many chances, played sublime winners, as well as clocking up naïve, frustrating mistakes. Kvitova, who could have won in two sets, hit eight aces, nine double faults, 35 clean winners and 45 unforced errors. Williams was was not quite as profligate, with five aces, seven double faults, 21 winners and 29 unforced errors.

Yet the lingering memory is of a contest of the highest quality, because, under pressure both of them invariably found something special to bring the crowd to their feet. The pivotal game on a see-sawing night was the ninth in the third set.

It was one of the most dramatic of the tournament. Williams led 40-love but Kvitova scrambled back to deuce. Williams double-faulted on her first game point, found a 120mph serve for another, netted the simplest of volleys for deuce, got a third game point with a blistering down the line forehand, dumped a forehand for the fourth deuce point, Kvitova hit long for game point again, put another backhand into the net – and Williams, finally, led 5-4.

Kvitova, serving to stay in the tournament, drop-shotted for 40-love, and held for 5-all. This was a crazy game of tennis. She had to do it again, and this time was untroubled. They went to the tie-break.

Now it got down to pure nerves. Williams nearly lost her peaked hat mid-rally, but not her cool, and led 5-1 when they crossed. Kvitova double-faulted, her ninth of the match, and Williams served for a place in the semi-final. She too double-faulted, her seventh. She stepped up again – and foot-faulted for the umpteenth time. Kvitova put her final return out, and they shook hands with cordiality at the net, a decorous conclusion to a match of almost unbearable tension.

Stephens’ win was easier on the nerves but no less engrossing. It put her in her second slam semi-final, her first at home. What more could she ask for after all she has been through?

After nearly a year to recover from foot surgery, Stephens only began hitting a ball again in May and reappeared on the tour at Wimbledon. Since then she has won 13 of 15 matches, the one over Sevastova the most significant by a margin.

In the Latvian world No17 – who put out Johanna Konta in the fourth round last year and Maria Sharapova at the same stage two days ago – Stephens had an opponent who is a throwback in the Justin Henin mould, a touch player with a sharp tennis brain and excellent anticipation. And she wins without big weapons; she had just the one ace in four matches before this quarter-final, and managed to double the tally.

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The contrast in style and attitude made for tremendous entertainment. Sevastova, who wins 53% of her points from deep, was loath to be tempted forward, but not so Stephens who prowled the net to excellent effect.

By the time they got to the tie-break – a first for both of them this tournament – their energy levels looked to be sapped to near zero, but they found something extra.

Stephens, whose serve had fallen as low as 66mph and had not managed an ace, looked to be at a disadvantage in the shootout, but she hit hard and sharply off the ground to cross at 3-all. A netted forehand handed Stephens two match points, and she sealed it with a backhand down the line to wrap up a match of the highest quality.

If the semi-final is anywhere near as good as either of these two tremendous quarter-finals, the tournament will edge towards a fitting climax, whoever makes the final.