She will play the victor of Tuesday's night match between Serena Williams and Karolina Pliskova in the last four.
Sevastova, who retired from tennis in 2013 due to injuries before returning in 2015, withstood a fightback from the 25-year-old American late in the match but sealed the win on her third match point when Stephens sent a backhand into the net.
Next up for Stephens, who at No. 3 is the highest seed left in the women's draw, is a repeat of last year's quarter-final against Latvian Anastasija Sevastova. Sevastova, forced out of the game by injuries in 2013 before launching a comeback almost two years later, showed some steely resolve, serving it out on her third match-point opportunity. "It was important that I won the first set".
Sevastova coped better with the challenging conditions to book her place in her first Grand Slam semifinal against the victor of the clash between Serena Williams and Karolina Pliskova.
"I think it was very physical today and tough to play", Sevastova said.
Stephens had used some obscene words out of desperaiton for not being able to execute her shots with pinpoint precision like in the other three rounds to win the match. I worked really hard on that instead of trying to hit a trick shot or do fancy stuff. The Spanish player marked her 30th birthday in style with a memorable 6-4, 6-3 win over the five-time Grand Slam champion whose last Grand Slam win was in Paris in 2014.
Thiem is aware of what he did well to defeat Nadal in the past but maintains that nobody's game matches up well against the world No. 1.
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Serena Williams shook off a slow start to grab eight consecutive games and beat 2016 runner-up Karolina Pliskova 6-4, 6-3 for a spot in the U.S. Open semifinals.
"Well I don't know", Williams said of how she engineered the turnaround.
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.
Novak Djokovic is aiming to make an eleventh US Open semi final tonight.
Indeed Stephens fought back to narrow the gap to 4-3, but Sevastova grabbed another break with a well-timed drop shot for a 5-3 lead and sealed the victory on her third match point when a tired Sephens put a backhand into the net. And when you're, like, winning a tournament, you think that's normal.
"It was an wonderful journey, this three, four years".
"I hope I will enjoy it, playing semi-finals".