Keys had lost each of her previous three competitive meetings with fellow American Stephens, including the final of the 2017 US Open.

This time Keys broke her duck, winning 7-6 (8-6) 4-6 6-2 in the WTA Premier event on outdoor clay courts in South Carolina.

“It’s always hard to play a friend, so on that side of it you’re obviously not going to be saying ‘come on’ in each other’s faces or anything like that,” she said of the top seed.

“But, I mean, we’ve been friends forever. So if she circles a mark and says it’s out, I’m going to believe her.”

Keys will face Monica Puig for a place in the decider, the Puerto Rican having surprised Danielle Rose Collins in straight sets.

In the other quarter-finals, 2011 winner Caroline Wozniacki eased past Maria Sakkari to book a meeting with Petra Martic, who upset Belinda Bencic in straights.

In the Monterrey Open, top seed Angelique Kerber, a two-time beaten finalist, defeated Kirsten Flipkens 6-2 6-4, and she will now tackle Victoria Azarenka in the last four. The Belorussian ousted third seed Anastasia Pavlyuchenkova, a four-time winner of this WTA International event, 6-0 6-4.

Title-holder and second seed Garbine Muguruza needed a second-set tie-breaker to get the better of Kristina Mladenovic, setting up a meeting with Magdalena Rybarikova in the semi-finals.

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