But Cilic suddenly rose to the occasion and deployed his ballistic forehand to get back on serve at 5-5 before securing the opener after an error-filled tiebreak by both players.
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The career-best Grand Slam performance for Sevastova comes after she retired from the sport in 2013 because of recurring injuries only to return in 2015.
Playing in punishing heat and humidity, with a sinus infection that has plagued her since the tournament began, Stephens shied away from excuses, saying she just didn't play well enough to win. After she won her first game of the second set, she let out a triumphant, Serena Williams-esque roar.
"The fact that I made it to the quarter-finals and played some really good matches and I just competed as hard as I could, I mean (there's) a lot to be proud of".
"I just play them instinctively, and that's how they work, or don't work sometimes".
The match on a sweltering Tuesday afternoon was a rematch.
Now comes a rematch: She'll face No. 19 Anastasija Sevastova of Latvia, the same person she beat in last year's quarterfinals at Flushing Meadows.
Stephens got back on serve from the shade once more but was unable to force a third set, as another break from Sevastova left her serving for the match, which she put to bed at the third time of asking.
Sevastova herself relies on variety more than power, and she caught a slow-moving Stephens with a number of drop shots and drop-shot lob combinations. "I wish I could have played better, but it just wasn't the day".
"When the shade was there it was so hot here and fantastic there", Sevastova said of the contrast of playing on the shady or sunny end of the court.
The Australian meets Novak Djokovic in the quarter-finals while Rafael Nadal beat Dominic Thiem to set up a semi-final showdown with Juan Martin del Potro. "Maybe the top 100".
"But in the end it's awesome, yes?" Right now you're in the tournament, you're playing next tournament next week, and you don't feel it. Past year he lost a very tough match against Del Potro here. The two will square off in the semi-finals on Thursday, with the 23-time major champion Williams starting as the firm favourite.