• US player lost 6-2, 6-3 to the world No 18 in scorching heat • Juan Martín del Potro beats John Isner in four sets

The reigning women’s champion, Sloane Stephens, succumbed to the tenacity of Anastasija Sevastova as well as the stifling heat and humidity that enveloped the Arthur Ashe Court as the upsets kept coming on day nine of the US Open.

Roger Federer complained about the humidity during his shock defeat by the Australian underdog John Millman in the early hours of the morning but there was the added dimension of burning heat in still, unforgiving air when Stephens and Sevastova stepped on to the same court at noon.

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The Latvian, ranked No 18 in the world, fully deserved her 6-2, 6-3 win, although Stephens fought all the way to the end when visibly suffering.

Where Stephens has used tennis to lift herself from adversity, Sevastova, introduced to the game by her grandmother, did not play competitively until she was 15, quit the sport in 2013, disillusioned with the grind of the Tour, and moved to Vienna, where she still lives, to study leisure management.

There was nothing leisurely about her performance on Tuesday, and she mixed delightful drop shots and chips with some rasping groundstrokes to torment the suffering champion.

This was Sevastova’s third quarter-final here in a row and she is in the semi-finals of a major for the first time. “It was very physical, so hot,” she said courtside. “The first set was crucial. I showed some nerves in the end but it’s normal. I stuck to my game plan, to move well and take my chances.”

Stephens dropped serve to go 3-1 down in the second set and, when Sevastova drop-shotted the American to go 40-love up on her serve, Stephens barely bothered to respond.

The heat was so intense, a boys match on Grandstand was suspended after only 36 minutes and 10 other junior matches were stopped.

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Back on Ashe, they had been playing for just over an hour. Then, on the point of collapse Stephens won eight points in a row to get back on serve. It was a monumental effort. A run of 11 consecutive points came to an end, though, when she netted a routine backhand volley.

Stephens saved break point and fought through four deuce points but could not reach another drop shot from Sevastova, who served out with new balls from the shaded end. It hardly seemed fair. Stephens saved two match points but dumped a tired backhand and it was done.

It takes a lot for a visiting player to win over an American audience playing one of their own but Juan Martín del Potro, who won here as a prodigy in 2009, was that man again on Tuesday when he beat John Isner 6-7 (5), 6-3, 7-6 (4), 6-2 in what he described as “impossible” conditions in the quarter-final.

“I’m so happy to reach another semi-final in my favourite tournament, which is very special to me,” the Argentinian said, drenched from his effort, to loud acclaim on court. “Of course beating John in this sort of match is epic. We both fought all the match. I survived with my serve at a couple of points.”

He dragged his 6ft 6in frame to the locker room in the mandated heat break after three sets and described how it got him through the final set. “I took a shower and re-taped my ankles, lay down on the table – and I did not want to come back. It’s impossible to play tennis in this heat but this crowd are great.”

Among the fans were a group of friends Del Potro had brought from Argentina. “If I meet them [before the semi-finals on Friday], it is dangerous for me. I will stay resting in my hotel, then afterwards we will have a chance to have fun together. They are so good.”

If anyone was biologically suited to move with maximum efficiency in the New York heat that has plagued most days of this tournament it surely would be del Potro and 6ft 10in Isner. They move like glaciers between points but find the after-burners when they need them.

Up two sets and 5-2 after nearly three-and-a-half hours, del Potro received a one-minute massage on his thighs during the last changeover for what looked like fatigue or cramping. Isner also had been close to seizing up more than once in the killing conditions.

Del Potro drove Isner to deuce twice on his last serve, fashioned match point with a belting forehand and was relieved to see his exhausted opponent put a concluding, wary forehand into the net.