Every round was a round closer for Stephens to defend her U.S. Open title from a year ago, but the steaming heat of the New York City summer and the sizzling shots of Sevastova had gotten the best of the number three femal tennis player in the world.
Stephens gave credit to her opponent, Sevastova saying "It's hard match and I though she played solid today and obviously the better player won".
"Last year I was almost one point away from doing that too", said Nadal, referring to his close five-setter with Gilles Muller in the Wimbledon fourth round last season.
"I try not to put too much emphasis on defending the title, just try to come in and win as many matches as possible - keep playing, keep going".
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.
"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".
Stephens would finally collect a break on her eighth opportunity, when Sevastova sent a forehand wide, serving at 2-0, 30-40 in the second set.
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The 5 set match lasted almost five hours.
This is a rematch of the French Open final, won by Nadal in June. "It's for semi-finals of US Open".
"But now, obviously when you win more, you have higher goals", she said.
"When you don't play big points well, the match can get away from you".
The 14-year-old comes into this tournament as the second-ranked junior in the world after winning the girls' French Open title earlier this year.
She earned the last of five breaks in the second set to take a 5-3 lead and served it out on her third match point when a tired Stephens put a backhand into the net. The two will square off in the semi-finals on Thursday, with the 23-time major champion Williams starting as the firm favourite. But Sevastova held her concentration and her serve before racing to break in the next.
Nadal was tested in his last two rounds, edging past Karen Khachanov in four close sets in round three, before dropping a set to Basilashvili on Sunday.