New York , United States (AFP) — Spain’s Pablo Carreno Busta cruised into his first Grand Slam semi-final and American Sloane Stephens matched her best Slam showing by reaching the last four yesterday at the US Open.

Carreno Busta, who has not dropped a set, downed Argentine 29th seed Diego Schartzman 6-4, 6-4, 6-2, while 83rd-ranked Stephens outlasted Latvian 16th seed Anastasija Sevastova 6-3, 3-6, 7-6 (7/4).

“I just told myself to keep fighting and stay consistent,” Stephens said. “I knew if I just stick with it and stayed in every point I knew I’d have my opportunity and I did.”

Stephens, who missed 11 months with a left foot injury before returning at Wimbledon, has won 13 of her past 15 matches entering a Thursday semi-final against a later winner between two-time Wimbledon champion Petra Kvitova and seven-time Grand Slam trophy-lifter Venus Williams.

“I’m getting teary-eyed,” Stephens said. “This is just incredible.

“When I started my comeback at Wimbledon I could never have dreamed of coming back and having these results and making the semi-finals at my home Slam. It’s indescribable.”

Carreno Busta, the first player to face four qualifiers in any Grand Slam, booked a Friday semi-final against either South African 28th seed Kevin Anderson or 17th-seeded American Sam Querrey, whose first Slam semi-final was in July at Wimbledon.

“Incredible,” 12th seed Carreno Busta said. “It’s something that I always dreamed about but something I never thought was going to arrive here. It’s a great feeling.”

While legends Roger Federer and Rafael Nadal are each one win from meeting for the first time at the US Open in a potentially epic semi-final, this half of the men’s draw is guaranteed to produce a first-time Slam finalist.

“It would be fantastic to play him in the final,” Carreno Busta said of Nadal. “But we have to play step by step.”

Carreno Busta captured the first set in 38 minutes, broke in the ninth game and held again to take the second. He broke at love on a double fault to open the third set, broke again in the seventh game and held to end it in just under two hours.

Stephens’ only prior Slam semi-final was at the 2013 Australian Open semis, while Sevastova matched her best major run from last year at New York by ousting Maria Sharapova to reach last eight.

In the tie-breaker, Stephens took four of the last five points, three on Sevastova errors before hitting a down-the-line backhand winner to win in two hours 28 minutes.

“I was able to play loose and ‘Bam’, here we are,” Stephens said.

US ninth seed Williams, the oldest women’s entrant at age 37, was seeking her third US Open crown after 2000 and 2001 and third Slam final of the year after Australian Open and Wimbledon runner-up finishes. She hasn’t reached three Slam finals in a year since 2002.

Williams would be the oldest US Open women’s semi-finalist and the oldest Slam semi-finalist since Martina Navratilova at Wimbledon in 1994.

Kvitova, who leads their career rivalry 4-1, is battling back from a five-month absence after injuring her left hand when attacked by a knife-wielding home intruder last December.

Four American women, also including Madison Keys and CoCo Vanderweghe, have reached the quarter-finals for the first time since 2002 and they could produce the first all-US semi-finals in New York since 1981.

“This is amazing and I hope there are four Americans in the semi-finals,” Stephens said.

What began as an eight-woman fight for the world number one ranking at the US Open is down to two.

Czech Karolina Plishkova, the reigning number one and last year’s US Open runner-up, must reach this year’s final or lose the top spot to already ousted Garbine Muguruza, the reigning Wimbledon champion.