Venus beats Kvitova, to face Stephens in US Open semis

US ninth seed Williams, seeking her third US Open crown, advanced to a Thursday matchup against 83rd-ranked compatriot Sloane Stephens for a spot in Saturday's final.

"I'm so fortunate to have won that match. It came down to the wire," Williams said. "I try to tell myself enjoy the competition, enjoy the battle and I think I was able to do that."

In the men's event, South Africa's Kevin Anderson reached a Grand Slam semi-final for the first time where he will face Spain's Pablo Carreno Busta who will also be appearing in his maiden last-four at a major.

Stephens, who missed 11 months with a left foot injury before returning at Wimbledon, matched her best Grand Slam showing by outlasting Latvian 16th seed Anastasija Sevastova 6-3, 3-6, 7-6 (7/4).

"This is just incredible," Stephens said. "When I started my comeback at Wimbledon I could never have dreamed of coming back and having these results. It's indescribable."

Stephens has won 13 of her past 15 matches and matched her 2013 Australian Open semi-final run for best Slam effort.

Williams, who improved to 2-4 all-time against the Czech 13th seed, will return to the world top five for the first time since January 2011, a span that saw her diagnosed with the energy-sapping disease Sjogren's Syndrome.

Williams, the oldest Slam semi-finalist since Martina Navratilova at Wimbledon in 1994, won the 2000 and 2001 US crowns. 

She was runner-up this year at Wimbledon and the Australian Open and could reach three Slam finals in a year for the first time since 2002.

Kvitova battled back from a five-month absence after a knife-wielding home intruder injured her left hand last December.

"I'm glad I'm still able to compete on the high level against the top players which I hope will give me some confidence to continue to play well, to know that it's still there somewhere," Kvitova said.

If Americans Madison Keys and CoCo Vanderweghe win Wednesday, they will produce the first all-American US Open semi-finals since 1981.

"That would be huge," Williams said. "I'd love that."

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

Legends Roger Federer and Rafael Nadal each practiced ahead of Wednesday quarter-finals in which wins by each would set up their first US Open meeting in an epic Friday men's semi-final.

The other half-bracket, however, will offer a first-time Slam finalist.

South African 28th seed Anderson downed 17th-seeded American Sam Querrey 7-6 (7/5), 6-7 (9/11), 6-3, 7-6 (9/7) to book a berth in Friday's semi-finals.

Anderson, the first South African in any Slam semi-finalist since Wayne Ferreira at the 2003 Australian Open, will meet Spanish 12th seed Carreno Busta, who has not dropped a set, for a place in Sunday's final.

"To play in one of the most famous courts in the world at night and to get through, it feels fantastic," said Anderson.

Carreno Busta, the first player in any Grand Slam to face four qualifiers, cruised into his first Slam semi-final by ousting Argentine 29th seed Diego Schartzman 6-4, 6-4, 6-2.

"Incredible," 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."

With Anderson standing 6ft 8in (2.02m) and Querrey 6ft 6in (1.97m), it was the tallest matchup ever so late in any Slam.

- 'I'm not a robot. Sorry.' -

Sevastova, who matched her best major run from last year at New York by ousting Maria Sharapova to reach the last eight, led 3-1 in the third set before Stephens rallied.

"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'd have my opportunity and I did."

In the tie-breaker, Stephens took four of the last five points, three on Sevastova errors before hitting a down-the-line backhand winner ensured her win to reach the top 35 in next week's rankings.

Sevastova admitted nerves got to her in the tie-breaker, saying, "It's normal. You play for semi-finals of US Open. I'm not a robot. Sorry."