Former World No.15 Kaia Kanepi continued her improbable comeback to reach her first Grand Slam quarterfinal since 2013, and her first at the US Open in seven years after knocking out Russian youngster Daria Kasatkina in two hard-fought sets.

NEW YORK, NY, USA - Not your ordinary qualifier, Kaia Kanepi reached her sixth career Grand Slam quarterfinal on Monday, dispatching Volvo Car Open champion Daria Kasatkina, 6-4, 6-4.

"I didn't expect this," she said in her post-match press conference. "I hoped to qualify and keep going, see what happened with my tennis. It's pretty amazing where I am now compared to where I was few months ago. It's great."

Into the second week at the US Open for the first time in three years, Kanepi's experience was on display against the crafty youngster, who had never been past the third round at any major tournament before this week. Using her big forehand to ruthless effect, the 32-year-old held especially strong on return, breaking serve to take each set and clinch the match after 87 minutes on court.

Kanepi was once a Top 15 player, whose big game brought her into the second week of multiple major tournaments - including at the USTA Billie Jean King National Tennis Center back in 2010 - before illness and injuries kept her away from the game's biggest stages for two years.

"I missed the adrenaline when I was at the tournaments. I missed winning. And I missed that feeling when you play well." - Kaia Kanepi

"I missed the adrenaline when I was at the tournaments. I missed winning. And I missed that feeling when you play well."

The Estonian began hitting again in January - in between driving through the treacherous ice roads in Finland - and had to play the qualifying tournament just to have a shot at the main draw, dropping just one set along the way.

Winning a rematch of a 2010 US Open encounter with Yanina Wickmayer in the second round she battled past another youngster in the third, recovering from a break down to defeat Naomi Osaka to reach the second week.

.@KanepiKaia reaches US Open 2017 QFs after a 6-4, 6-4 win over Kasatkina. Sheplays winner of Keys-Svitolina https://t.co/ieWxgOYKfD #usopen pic.twitter.com/TXBqrVnzyo — US Open Tennis (@usopen) September 4, 2017

Across the net was Kasatkina, who dismissed former junior rival and reigning Roland Garros champion Jelena Ostapenko in straight sets to enjoy a full circle moment at the US Open, having made her first Grand Slam third round at this very tournament two years ago as a lucky loser.

"I was expecting her to play her best tennis because it's the fourth round of a Grand Slam and she's a very good player," Kasatkina said after the match. "I was trying to my best, fighting to the last point.

"She was putting a lot of pressure on me, and I was trying to play more contrast. There's no time to think with her, because you don't have any time."

Still, the 20-year-old Russian didn't have enough answers to Kanepi's big game, which let loose 34 winners and 43 unforced errors; Kasatkina managed 11 winners to 22 errors of her own.

"There've been a lot of ups and downs this season, so I'm happy to show my best result at a Grand Slam. I'll try to come back better, and go even further in my next tournaments. I want to forget this match, even the tournament because everything is still going on."

Standing between Kanepi and a long-awaited maiden Grand Slam semifinal is the winner of the final Round of 16 clash between 2015 Australian Open semifinalist Madison Keys and No.4 seed Elina Svitolina, one of three remaining women still in the running towards becoming the WTA's next top-ranked player alongside Karolina Pliskova and Garbiñe Muguruza.

"She's aggressive," Kanepi said of Keys. "It's really tough to say more, because she hits hard and she wants to win points fast. And I'm the same.

"[Svitolina] plays more. She makes less mistakes. But I haven't played her for a long time, and I haven't played top players for a very long time. I don't know yet what to expect."

Though Muguruza lost her fourth round match against Petra Kvitova, the Spaniard is still in pole position to ascent to No.1 provided Svitolina falls before the semifinals and Pliskova falls before the final. Should Pliskova play Svitolina in the semifinals, Muguruza would be eliminated from No.1 contention and the winner of that match would become WTA World No.1.