Venus Williams and Petra Kvitova shake hands a the end of their match/ Twitter

Venus Williams has reached her 23rd Grand Slam semi-final after a thrilling win over Petra Kvitova in a final-set tie-break.

The 37-year-old American won 6-3 3-6 7-6 (7-2) in front of a rapturous night-session crowd in New York.

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“I was so fortunate to win that match. It came down to the wire and I’m hoping we have more matches like that,” said Williams.

She next faces Sloane Stephens the last four.

An all-American semi-finals looks possible with Madison Keys and Coco Vandeweghe hoping to join their compatriots in the last four when they play their quarter-final games on Wednesday.

“I would love the top four, five to be that (American) again,” added Williams. “That would be huge.”

Remarkable

27-year-old Kvitova missed out on a first US Open semi-final, ending a remarkable run just nine months since she suffered a knife attack at her home, which left her requiring surgery to her playing hand.

“Everything she has gone through is unbelievable,” said Williams.

“It’s wonderful to see her back and playing. I was so excited to see her playing well, to be able to play her.”

The pair had met five times before and each time they had needed three sets, twice a final-set tie-break, and once again there was nothing between them.

Venus Williams was 15 years younger – just 22 – the last time she made three Grand Slam semi-finals in a single season.