Karolina Pliskova, the No. 8 seed, knocked off Williams in the 2016 semifinals before the 23-time Grand Slam champion missed last year's tournament, when she gave birth.
"So the fact that I made it to the quarterfinals and played some really good matches and I just competed as hard as I could, I mean [it's] a lot to be proud of". It's tough to play, so hot in here.
She raced to a 3-0 lead in the first set and then 4-0 in the second against the shaky Tsurenko, who finished with more unforced errors than points in her first major quarterfinal.
The players took a 10-minute break at the end of the third set, and Del Potro said: "I lay down on the table and I didn't want to come back again because with this heat it's impossible to play tennis".
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"I hope that I can go to Asia and win some more matches and hopefully make the year end and hopefully keep going as far as I can". After she won her first game of the second set, she let out a triumphant, Serena Williams-esque roar.
"He's maybe playing some of the best tennis ever right now for him", said the American.
Serving for the match, the Latvian raced out to triple match point and although Stephens saved two of them, Sevastova sealed the win when the 25-year-old American pushed a backhand into the net.
"You have to appreciate it more", she said. This year, Keys also remains alive as of now, taking her round of 16 match in straight sets. "I ran back and hit a forehand cross-court - and the crowd went insane", she said.
Sevastova's creative play makes for a great matchup with Stephens, as their intense, three-set battle here previous year demonstrated. For his part, Federer has not played poorly; he made it to the final in Cincinnati just before the start here in NY but was overwhelmed by a surging Novak Djokovic.
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Williams did drop her serve once in the second, coughing up one of her five double faults on break point as Pliskova narrowed the gap to 4-1.
Thiem chuckled when he was asked about Nadal's apology but added that now that he was out of the tournament, he would love to see Nadal defend his title.
It was already 2.04am and four hours and 49 minutes into the tightest of matches when he finally overcame Dominic Thiem, edging a sudden death shootout to make tomorrow's semi-finals at Flushing Meadows.
It was the middle of the night before the Spaniard could head home after beating Thiem: 'It was a great match, great atmosphere and I was happy to be part of it. As usual, he had to do it without the benefit of many cheap points; he hit just three aces, 15 fewer than Thiem.
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I have had three surgeries and every time I had extreme doubts over whether I would get back. "I have prayed for that". Elsewhere in the men's bracket, No. 7 seed Marin Cilic moves on to meet No. 21 seed Kei Nishikori in a quarterfinal.