Home favourites Venus Williams and Sloane Stephens both came through third set tie breaks to set up an all-American semi-final at the US Open.

Williams, a two-time champion in New York, was involved in a late night thriller on the Arther Ashe Stadium, eventually prevailing 6-3 3-6 7-6 (7-2) over Czech Petra Kvitova.

In front of a packed crowd, the 36-year-old recovered from 3-1 down in the final set before sealing the victory in two hours and 34 minutes.

"I didn't want to let you guys down"

"I was so fortunate to win that match," said Williams in her on-court interview. "It came down to the wire and I'm hoping we have more matches like that."

"I have to say I felt every single one of you guys behind me, all 23,000," she told the crowd afterwards. "I didn't want to let you guys down."

Williams will now face her compatriot Stephens in the last four after the latter defeated Latvian Anastasija Sevastova, Maria Sharapova’s conqueror, 6-3 3-6 7-6 (7-4).

Stephens comeback better than imagined

The 24-year-old American, who missed last year’s tournament with a foot injury, also came from a break down in the decider to reach her first semi-final in New York.

Stephens only returned to the tour in June after undergoing an operation at the start of the year and has subsequently slipped down to 83 in the WTA rankings.

"I'm getting teary eyed, this is incredible," she said after the match.

"When I started my comeback before Wimbledon, I could have never even dreamed of having these results in my home Slam, at my favorite tournament. It's indescribable."

There is still a possibility that America could boast all four semi-final spots in the women’s singles event.

Tonight, Coco Vandeweghe faces top seeded Czech Karolína Plíšková while Madison Keys, coached by former US Open champion Lindsay Davenport, takes on Estonia’s Kaia Kanepi.

Querrey's hopes ended by Anderson

However, there will be no representatives from the home nation in the last four of the men's event, following Sam Querrey’s defeat to 28th seed Kevin Anderson.

Querrey was the only man in the bottom half of the draw who had previously reached a major semi-final, following his impressive run at Wimbledon earlier this year.

Even so, the 29-year-old Californian came out second best in a battle between two big servers.

Anderson, who beat Andy Murray at this event two years ago, won 7-6 (7-5) 6-7 (9-11) 6-3 7-6 (7-9), in a match which yielded 42 aces in total.

The South African will now face Spaniard Pablo Carreno Busta for a place in the final, after the 12th seed swept aside diminutive Argentine Diego Schwartzman 6-4 6-4 6-2.