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 and second seed Caroline Wozniacki have taken turns being No. 1 this year with Wozniacki grabbing it after beating Halep in three sets in the Australian Open final and Halep winning it back just prior to Indian Wells.
Simona Halep (ROU) during her second round match against Caroline Dolehide (not pictured) in the BNP Paribas Open at the Indian Wells Tennis Garden.
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.
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She said Serena Williams - who made her return at this year's tournament after having a baby in September - "should have been seeded number one, because she left as number one in the world".
The thought of going out in the fourth round, she said in the post-match interview, got in her head so she gave Vondrousova some unexpected hope.More news: Major events in Trump's decision to fire Tillerson
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Halep won this event in 2015 and Wozniacki won it in 2011.
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 Halep in the final.
But the 25-year-old Czech showed all her experience to set up a meeting with Naomi Osaka of Japan after she overcame unseeded Maria Sakkari 6-1 5-7 6-1.
The writing was on the wall for Wang when she also lost the first three games of set two. She was the last Chinese singles player standing in the California desert. I think this will change a little bit in the future, but for sure the game is good and not really any weakness.
Kasatkina improved to 11-6 on the WTA Tour season as she seeks to better her quarter-final appearance here in 2016. It was the first time Venus has beaten Serena since 2014 in Montreal.
Williams, who is the oldest female player in the draw at 37, rallied back in the second set to book her spot in the quarter-finals.
Pliskova's 6-1 7-6 (2) win ended the run of the young American, a wild card who beat ninth seed Petra Kvitova in the third round for the biggest win of her fledgling career.