Women's world number 1 Simona Halep safely progressed into the quarter-finals with a convincing 7-5, 6-1 victory against Wang Qiang.
She will next play un-seeded Petra Martic of Croatia, who overcame Marketa Vondrousova 6-3, 7-6 to progress.
The 2018 Australian Open finalist is one of the two former champions left in the draw and has won 17 out of 18 matches in this season.
2018 BNP Paribas round-up
Halep bats for Serena
According to a report, Simona Halep feels that tennis authorities should have a protected seeding system for players returning after maternity leave. She felt Serena Williams should have been seeded number 1 as she left in the same position last year before leave.
Big guns through
Wins for Venus, Plisokova, Wozniacki stunned
There were wins for veteran Venus Williams and former world No. 1 Karolina Pliskova.
Venus, who conquered sister Serena in the previous round, was given a stern test from Latvia's Anastasija Sevastova but she won 7-6, 6-4.
Meanwhile, 5th seed Pliskova beat Amanda Anisimova 6-1, 7-6. Pliskova will face Japan's Naomi Osaka.
Caroline Wozniacki was stunned by 20-year-old Russian Kasatkina 6-4, 7-5.
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India's Yuki Bhambri's run comes to an end
Yuki Bhambri's strong run at the Indian Wells came to an end but not without him giving a stern fight.
The gritty men's singles player bowed out of men's third round after going down in three sets against 18th seed Sam Querrey.
Bhambri won the first set 7-6, but Querrey hit back to win the next two 6-4, 6-4.
Bhambri is world number 110.
Other men's singles results
In the men's singles event world number 3 Marin Cilic suffered a shock 4-6, 4-6 defeat in straight sets to Philipp Kohlschreiber. Meanwhile, senior Juan Martin del Potro ascended higher by overcoming Spain's David Ferrer 6-4, 7-6. He would next face fellow Argentine Leonardo Mayer.
Wife accuses Indian pacer, Mohammed Shami of fixing matches
Paes named in India's Davis Cup squad