Petra Kvitova fended off home favourite Madison Keys to reach the Western and Southern Open final and secure a return to the world's top 20.

The two-time Wimbledon champion battled to a 6-7 (6-8) 6-4 6-3 victory in two hours and 18 minutes, saying the match had been "mentally so tough".

Both players had taken significant scalps to reach this stage, with Keys knocking out world number one Iga Swiatek and Kvitova ousting Wimbledon runner-up Ons Jabeur.

Kvitova reached semi-finals at Cincinnati in 2012 and 2018 and lost three-set battles on both occasions, but this time she came good in the decider to earn a first final appearance at the event and a 40th overall in her WTA career.

The 32-year-old Czech slipped an early break adrift in the opening set before fighting back to force a tie-break. She came from behind in that, too, to level up at 6-6, only for hard-hitting American Keys to win the next two points, the first with a sizzling backhand winner.

Kvitova sensed she was still firmly in the match, however, and surges to 3-1 in each of the next two sets provided the platform to fully turn around the contest.

A 12th WTA 1000-level final awaits her, and she will go to 20th in the rankings should she lose Sunday's final and up to 15th if she carries off the title.

Kvitova said of her win: "It was incredibly tough. I expected it would be tough, but I didn't expect it that tough. Madison played unbelievable.

"She played an amazing tie-break, but I tried to keep going, be there and be a little calmer than before and wait for the chances. It was an incredible match, and I'm really happy that I made it somehow.

"I don't really care about the ranking. Being in the final, that's more important, and that's why I'm playing tennis: to be in finals and fighting for a trophy."

She awaited the winner of the second semi-final between Aryna Sabalenka and Caroline Garcia.

Madison Keys stunned top seed Iga Swiatek 6-3 6-4 to book her place in the quarter-finals of the Western & Southern Open on Thursday.

Keys arrived in the contest seeking a first career victory over a reigning world number one in six attempts, having failed to win a set in each of the previous five.

The 2019 champion had also lost her previous two showdowns with Swiatek, including a resounding 6-1 6-0 defeat in the Indian Wells Open quarter-finals earlier this year.

After the first games went with serve, Keys went into overdrive; reeling off nine successive games to take full command of the contest at 6-3 5-0.

Swiatek rallied as she rescued match point to avoid the bagel, winning 11 of 12 points to reduce the second-set deficit to 5-3.

The winner of six WTA titles this season, the Pole saved a further match point in the ninth game before claiming what appeared to be another crucial break of serve.

However, former US Open finalist Keys responded magnificently to make it third time lucky against Swiatek, who is now 4-4 since her 37-match winning streak ended with defeat by Alize Cornet at Wimbledon.

The prize pot for this year's US Open will top $60million for the first time in the competition's history, event organisers have announced.

The 2022 edition at Flushing Meadows gets under way on August 29 and runs for just under two weeks.

It was revealed on Thursday that $60m will be up for grabs, topping the previous record of $57.5m from last year, with both singles champions to receive $2.6m.

Players will be given $80,000 for making the main draw and $121,000 should they make it to the second round. Runners-up in the singles will pocket $1.3m.

In the doubles, the champions will receive $688,000, the runners-up $344,000 and the semi-finalists $172,000.

Emma Raducanu admitted she has been "too tense" in recent defeats and is aiming to play more freely as she prepares to defend her US Open title.

Raducanu has struggled to follow up last year's shock win at Flushing Meadow, but she appears to have hit form at just the right time.

The 19-year-old has beaten both Serena Williams and Victoria Azarenka in straight sets during this week's Western and Southern Open in Cincinnati, dropping just four games against Williams and two against Azarenka.

Her win against Azarenka on Wednesday was just Raducanu's third career victory against a top-25 opponent, after beating Belinda Bencic and Maria Sakkari on her way to winning last year's US Open.

Speaking after her win against the Belarusian, Raducanu said: "I think I have tried a lot of things, and this year I think some matches, I have lost a lot of matches from leading situations and probably just played too tense.

"I think that I just need to swing, and I just said that these two tournaments, or this tournament especially, I'm just going to swing freely and take that and see what happens."

Raducanu also said she will wait until after the tournament to reflect on beating two multiple grand slam champions with relative ease.

"I think after the tournament I actually have to take a step back and be like, 'Look, you just beat two unbelievable champions'," she said. "It's a pretty good achievement. You know how difficult the wins are to come by."

The number 10 seed will face seventh seed Jessica Pegula in the third round in Cincinnati on Thursday.

Serena Williams is "one of the greatest of all time", says fellow tennis legend Rafael Nadal as the 23-time grand slam winner prepares to hang up her racquet.

The 40-year-old, one of the most decorated players in the history of the sport, signalled her intent to "evolve away" from the game in an interview with Vogue Magazine earlier this month, hinting at her retirement following the U.S. Open in September.

With just shy of two-dozen grand slam singles titles, Williams trails only Margaret Court for the all-time record of 24 crowns, and could equal her in her farewell appearance.

Nadal, meanwhile, lies one behind her after victory in the Australian Open and French Open this year took him clear of Novak Djokovic and Roger Federer to 22, though the former's win at Wimbledon has seen him close the gap again.

The duo are set to feature at this week's Western and Southern Open, where Williams will face incumbent U.S. Open champion Emma Raducanu, and the Spaniard - who will mark his return from injury - has nothing but praise for his fellow giant of the game.

"She is one of the greatest sports [people] of all time," he stated. "I feel lucky to share a tour for a long period of time with her.

"Of course, from a selfish point of view, it's sad that she's leaving the tour but, on the other hand, we can't thank her enough for all the things that she did for our sport.

"I think she's an amazing inspiration for a lot of people around the world and I think she deserves to choose whatever works for her better at this stage of her life.

"So I wish her all the best. Hopefully, we can keep seeing her around the tour because I always believe that our sport, or the sport in general, is bigger and better when legends are around and she is a legend.

"Hopefully, we can enjoy her in a different way around the tour."

Nadal was forced to withdraw ahead of the Wimbledon semi-finals earlier this year with an abdominal tear, and now faces a potentially nervy run through to the U.S. Open in terms of fitness.

But the 36-year-old is cautiously optimistic, adding: "I hope to be ready. That's what I'm trying to do. Try to be a little more conservative, but I hope I can be ready to play.

"Of course, I need some more days to analyse how things are going in terms of abdominal feeling.

"But things are going well for the moment, so hopefully I can manage to be ready. I'm excited. I want to play tennis again on the tour. I'm having a good season, I'm enjoying it, so I want to enjoy this week in Cincinnati."

Simona Halep secured victory against Beatriz Haddad Maia in the Canada Open final on Sunday, though was given a tougher test than she had otherwise experienced throughout the tournament.

The Romanian was a 6-3 2-6 6-3 victor, dropping a set for only the second time in the week, but standing firm in the clash that clocked in at over two hours.

That meant records for Haddad Maia, who has played the most WTA-level matches with three sets in 2022 (20) and spent over 12-and-a-half hours on the court at the Canada Open in 2022, more than any other player in a single WTA tournament this year.

Wimbledon semi-finalist Halep proved to be a step too far for the Brazilian, however, with the win marking her most significant honour since winning in Rome in 2020.

It was far from a vintage performance from the 30-year-old, who had nine double-faults in the match compared to Haddad Maia's two and left the door open for the South American - who was vying for victory in her first ever WTA 1000 event.

Halep had already clinched a return to the world top 10 by reaching the final in Toronto, the first time since her 373-week stint ended just over a week ago - which led to admissions that she considered calling it quits amid her decline.

A valiant comeback in 2022 has been one of the major stories of the calendar year though and, on the back of victory in Canada and a semi-final march at Wimbledon, will have high hopes for the U.S. Open.