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.
Halep advances to the quarter-finals and will face unseeded Petra Martic of Croatia, who advanced to the last eight with a straight sets 6-3, 7-6 (7-4) win against Czech Marketa Vondrousova on Tuesday.
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Halep needed just 76 minutes on the main stadium court to dispatch Wang as she won 64 percent of her first-serve points and broke Wang's serve seven times.
Halep won a title at the Indian Wells Tennis Garden in 2015 and Wozniacki won it in 2011.
Halep said she thought Williams "should have been ranked as she left".
Kerber thus extends her head-to-head lead over Garcia to 4-2, and avenges her loss to the Frenchwoman in their most recent match - a first-round encounter a year ago at the Dongfeng Motor Wuhan Open that kickstarted Garcia's run to back-to-back titles in Wuhan and Beijing and a spot in the Top 10. But as I say, if you want to be on the top, you have to beat the top players.
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".
"So it was a good chat".
"She has everything in her game". She was the last Chinese singles player standing in the California desert. "I wasn't missing that much".
Chahbahar project not aimed at strangulating anybody: Iran
The port is a crucial part of India's plans to create a transport and trade corridor to landlocked Afghanistan bypassing Pakistan. Iran and Pakistan have great relations that is going to be better in the future, said the representative of Pakistan in the UN.