Sloane Stephens reached a second Grand Slam semi-final of her career, edging out Anastasija Sevastova in a thrilling US Open quarter-final.

In the first of four women’s quarter-finals, all of which feature an American player, it was the 24-year-old from Florida who gave the crowd what they wanted with a 6-3 3-6 7-6 success that continues an unlikely comeback.

Stephens, a semi-finalist as a teenager in Australia in 2013 when she beat Serena Williams in the last eight, only returned to practice in May and competitive tennis at Wimbledon after foot surgery in January and an 11-month absence.

Playing under her protected ranking, she has produced a stunning story that has now accounted for three seeds – Dominika Cibulkova, Julia Goerges and now 16th seed Sevastova.

She will next face Venus Williams, who beat Petra Kvitova in Tuesday’s second quarter-final under the lights on Arthur Ashe Stadium.

The afternoon belonged to Stephens, who after her operation earlier this year was working as a reporter for the Tennis Channel. She has now won 13 of her last 15 matches, making the last four in Toronto and Cincinnati and now earning a first semi-final place in her home major.

Sevastova, who accounted for Maria Sharapova in the fourth round, made her fight every inch of the way, battling back from a couple of medical time-outs for treatment to a leg injury to level the match and lead by a break in the decider.

Stephens had looked the more composed in the early exchanges and with Stevastova clearly troubled by her injury, the American claimed the first set in 46 minutes

With Sevastova attempting to keep the rallies short and mix up her game, perhaps protecting her injury, it was Stephens who wilted and Sevastova levelled the match by claiming the set courtesy of a break in the fourth game when she had looked at her lowest ebb.

The Latvian moved into a 3-1 lead with another break early in the third and had points for a double break, only to see Stephens rally and then produce a break of her own to level up at 3-3 to the delight of those in attendance on Arthur Ashe.

With the crowd increasingly vocal and sensing their chance to play a part, the pair traded breaks again before holding comfortably on route to the tie-break where it was Stephens who kept her composure to claim her place in Thursday’s semi-finals.

I am getting teary-eyed, it is just incredible, she said in her on-court interview.

When I started my comeback at Wimbledon, I could never ever dreamed of something like this happening – making the semi-finals of my home slam and my favourite tournament. It is indescribable.

I’ve been playing well and consistent and staying calm on the court.

Before I started winning matches, I was really worried about my protected ranking and not having enough tournaments or being able to play.

There were so many things I was worried about but I realised I have it good. I play tennis and I have fun every day, that seemed to relieve a lot of stress and I have been able to play loose and play my game and here we are.

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(c) Sky News 2017: US Open 2017: Sloane Stephens into US Open semi-final for first time