Third seed Coco Gauff served up 17 double faults but still managed to beat China’s Yuan Yue 6-4 6-3 at Indian Wells on Thursday to reach the semi-finals in the Californian desert for the first time.

A day after her 20th birthday, Gauff had to rally from 3-1 down in the second set before setting up a clash with ninth seed Maria Sakkari, who ended American Emma Navarro’s run with a 5-7 6-2 6-4 victory. “I’m really happy to be through today’s match,” said one-time teen prodigy Gauff.

“It wasn’t the best style of the serving, but overall I think when it comes to the groundstroke game and returns, everything else, honestly, I played well. I’ll just try and take the positives into the next match.”

Gauff, who said she celebrated her birthday with steak tacos, saved seven of the 10 break points she faced over the match, including three to avoid going 4-1 down in the second set.

“I pretty much just relied on me just out-rallying her and being aggressive,” Gauff added. “I think a lot of break points that were saved, at least in that second set, I just remember hitting a lot of forehand winners.”

Gauff joined Iga Swiatek and Caroline Wozniacki as the only players to have reached five WTA 1000 semi-finals before the age of 21. Top seed Swiatek earlier also reached the semi-finals after former world number one Wozniacki retired with a foot injury early in the second set of their quarter-final.

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Wozniacki started strongly as she raced into a 4-1 lead but she was soon left frustrated as Swiatek produced a barrage of winners to storm back and win the set 6-4.

The Dane, who returned to the circuit last year after taking a three-year break to start a family, had a medical timeout to have her right foot re-strapped at the end of the first set.

That failed to improve the situation, however, and she gestured to her opponent that she was unable to continue once Swiatek had taken a 1-0 lead in the second.

“I have a huge respect for her and I’m sad she has to go that way, I’m sure she will recover and I hope she will be ready for Miami,” Swiatek said.

“But I’m happy that I played well enough in first set to win it.” Swiatek, the 2022 champion, will face Marta Kostyuk in the semi-finals after the Ukrainian defeated Anastasia Potapova 6-0 7-5. “Let’s not put expectations too high,” world number 32 Kostyuk said of her meeting with Swiatek.

“She’s a great competitor, she’s been on top of the game for two years already.”

Sakkari, who is working with new coach David Witt for the first time at Indian Wells after a patchy run of results, closed out the evening with a comeback win over Navarro to reach the semi-finals of the tournament for a third straight year.

“That was the toughest match I’ve played in a while,” said Sakkari. “Emma is an incredible player … She’s been playing amazing. It’s a huge win. I’m very happy I found a way to win this match today.”