NEW YORK (AFP/REUTERS) - Sloane Stephens, who missed 11 months with a left foot injury before returning in July, reached her first Grand Slam final by outlasting Venus Williams 6-1, 0-6, 7-5 on Thursday at the US Open.

Stephens, whose best prior Slam run was to the 2013 Australian Open semi-finals, will meet Madison Keys, who beat US compatriot CoCo Vandeweghe 6-1, 6-2, for a shot at the top prize of US$3.7 million (S$4.95 million).

"I just worked my tail off and tried to run every ball down and here we are," Stephens said. "It required a lot of fight and a lot of grit."

Stephens, who was ranked 957th in July when her hard-court campaign began, has won 14 of her past 16 matches, including semi-final runs at Toronto and Cincinnati, for a total of US$310,000 this season.

Ousting a seven-time Grand Slam champion who was seeking her first US Open final since 2002 left Stephens stunned.

"I have no words to describe what I'm feeling, what it took to get here, the journey I've been on," Stephens said. "It's incredible. I don't know how I got here. Your guess is as good as mine. Just hard work. That's it."

Now 83rd, Stephens is the lowest-ranked Slam finalist since unranked Justine Henin at the 2010 Australian Open and the lowest at the US Open since unranked Kim Clijsters won the 2009 title.

US ninth seed Williams could not overcome 51 unforced errors that doomed her bid to become the oldest women's singles finalist in US Open history at age 37.

"It was definitely well competed," Williams said. "In the end she won more points than I did and that's what it added up to.

"Just made so many errors at the end there... I wasn't playing well. Just wasn't playing well."

Williams will return to the top five in Monday's world rankings for the first time since 2011, the year she was diagnosed with strength-sapping Sjogren's Syndrome.

Stephens, who beat Williams in the first round of the 2015 French Open in their only prior meeting, will jump into the world top 25 next week with the victory.

A first-time career Slam champion is assured with Keys and Vandeweghe, who are good friends off the court, also having gone no deeper than a Slam semi-final.

Vandeweghe, seeded 20th, reached her only prior Slam semi-final in January's Australian Open while 15th seed Keys made her lone last-four major at the 2015 Australian Open.

"I feels amazing, these are moments growing up you dream about," said Keys. "It was one of those days where I came out and I was in a zone and forced myself to stay there.

"I had to rise to the occasion and I'm just happy to be in the final.

"Sloane is a new person right now, I think she is loving being out on the court again and she's obviously playing really well."

Vandeweghe admitted she had been outclassed in the semi-final.

"She was playing a great first set," said an emotional Vandeweghe, breaking into tears during her post-match media conference.

"I thought at some point she might start running a little bit colder than what she was doing. I mean, it's really not over until the last point.

"I was fighting as hard as I could for as long as I could, but she stayed hot the whole time."

It is the first all-American US Open women's semi-finals since 1981 and the first at any Slam since Wimbledon in 1985. Saturday will be the first all-American US Open women's final since Serena Williams beat Venus in 2002.

Williams netted a forehand to surrender a break and a 3-1 lead, was broken again in the sixth game and dropped the first set in 24 minutes. She had 17 unforced errors in the set and won only 13 points, just seven on her serve.

But in the second set, Williams denied Stephens on three break points and dominated to claim the set in 30 minutes to force a third.

Stephens broke to open the final set but Stephens surrendered a break on a wide backhand to lift Williams level at 2-2 and they traded breaks in the seventh and eighth games as the tension grew.

Stephens broke at love for a 6-5 lead - her lob and forehand crosscourt volley winners followed by a Venus backhand and forehand wide - and held to end matters after 2hr 7min.

Stephens is 4-0 in WTA finals, having won titles in 2015 at Washington and last year in Auckland, Acapulco and Charleston.

Stephens is 1-0 against Keys.