Indian Wells — World No1 Simona Halep and Venus Williams punched their tickets to the Indian Wells quarterfinals, while Caroline Wozniacki suffered another exit at the hands of Russia’s rising star, Daria Kasatkina.

Halep breezed through her fourth-round match with a 7-5 6-1 win over China’s Wang Qiang and eighth-seed Venus Williams faced a stern test from Anastasija Sevastova but held on for a 7-6 (8/6) 6-4 victory.

Kasatkina, who has beaten all four reigning Grand Slam champions in the past year, continued her giant-killing form with a 6-4 7-5 shock victory over world No2 Wozniacki. She recorded her second straight win over Wozniacki, having also beaten the Australian Open champion at the St Petersburg tournament in February.

She outsmarted me today. But at least I tried, and I tried to do what I thought I needed to do out there today. I just couldn’t execute as well as I wanted to.
Caroline Wozniacki

"I’m playing my best matches against the best players. But if you want to be on the top, you have to beat the top players," said the Russian.

Kasatkina improved to 11-6 on the WTA Tour season as she seeks to better her quarterfinal appearance here in 2016.

She hit one ace, won 54% of her first serves and broke Wozniacki’s serve six times in the 1hr 40min match.

"She outsmarted me today," Wozniacki said. "But at least I tried, and I tried to do what I thought I needed to do out there today. I just couldn’t execute as well as I wanted to."

It was a disappointing exit for Wozniacki, who finally silenced her critics earlier in 2018 with her maiden Grand Slam title in Melbourne, where she defeated Halep in the final. Wozniacki had a chance to get the No1 back but she needed to win the Indian Wells title to do it. Kasatkina said she was starting to believe in herself, especially when she faces top 10 players.

"In the beginning it was really tough because I was really nervous going on the big stages against big players. But now with experience and with time I’m getting into it. I’m getting pretty confident at this level. But I am still young so I have to work on everything."

Kasatkina next plays 10th-seed Angelique Kerber, of Germany, who roared past seventh-seeded Caroline Garcia 6-1 6-1.

Meanwhile, Halep, who is one of two former champions left in the draw, is now 17-1 on the season having already won a title in both singles and doubles at Shenzhen, China.

Halep advances to the quarterfinals where she will face unseeded Petra Martic of Croatia, who beat Czech Marketa Vondrousova 6-3 7-6 (7/4).

Halep called for a time-out in the first set so her coach, Darren Cahill, could come to the court to discuss strategy. "It was really important, because he just told me what I have to do. I knew that I had to change something, but I didn’t realise what it was exactly," she said. "So it was a good chat. I did exactly what he said after that."

At the same time Williams survived a difficult fourth-round test to beat Latvia’s Sevastova 7-6 (8/6) 6-4 just one day after beating sister Serena in a third-round contest. It was the first time Venus has beaten Serena since 2014 in Montreal.

"It was not an easy match to figure out," Venus said of her Tuesday victory. "She has everything in her game. And it was a quick comeback from yesterday, where you have the emotions of: ‘Hey, this feels like a final. But guess what, you’re only in the fourth round’."

Venus next faces Carla Suarez Navarro, who rolled past Danielle Collins 6-2 6-4.