World number one Simona Halep cruised past Wang Qiang of China 7-5, 6-1 in the fourth round of the WTA Tour's Indian Wells tournament on Tuesday (Mar 13).
It was a disappointing exit for Wozniacki, who finally silenced her critics earlier this year with her maiden Grand Slam title in Melbourne, where she defeated Simona Halep in the final.
Kasatkina will play either seventh seed Caroline Garcia of France or Angelique Kerber of Germany in the quarter-finals.
Although Halep's own performance was far from faultless, particularly in the first set, the Romanian triumphed 7-5 6-1 and will now face Petra Martic in the last eight.
Halep's coach, Darren Cahill, tweeted during a conversation with former world number one Chris Evert that returning female tennis players "should not be penalised for giving birth by starting from zero".
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Halep needed just 76 minutes on the main stadium court to dispatch her practice partner Wang as she won 64 percent of her first-serve points and broke Wang's serve seven times.
Only Wozniacki can usurp her atop the WTA rankings after Indian Wells, but she must win the title and hope Halep lose before the final.
She is now an impressive 17-1 this season having already won a title in both singles and doubles in Shenzhen. But as I say, if you want to be on the top, you have to beat the top players. "I did exactly what he said after that". Along with Iva Majoli, at 16 years and 199 days, Anisimova is the youngest player to reach the R16 at Indian Wells. "I dominated a little bit more".
To reinforce their hopes, Venus has to beat Carla Suarez Navarro or wildcard Danielle Collins in the quarterfinals. Playing the BNP Paribas Open for the second time, Osaka improved her best result in a Premier Mandatory event and became the first Japanese to make the quarter-finals here since 1996 when Kimiko Date lost to Martinez in the semifinals.
Fifth seed Karolina Pliskova ended teenage American Amanda Anisimova's run with a 6-1 7-6 (7-2) victory.