However, after Osaka’s shock departure in the third round in Miami, Halep will go back into the most effective when she chooses the title.
She next faces Venus Williams, that sailed past 14 th seed Daria Kasatkina.
American seven-time Grand Slam winner Williams beat the 21-year-old Russian 6-3 6-1 in just under 75 minutes Sunday to reach the fourth round.
She’ll go top of these ranks if she reaches the final and loses to anybody other than Czech world number two Petra Kvitova. Kvitova confronts France’s Caroline Garcia in the fourth round.
It took her almost three hours to beat 28-year-old Hercog, the planet 9 3 out of Slovenia.
“She played incredible and it was such a challenging match,” said Halep. “It was good to play almost three hours though. I slowly found my rhythm but I always had belief so when I can keep doing so, I will have a good tournament.”
World number one Osaka was conquered by 27th-seeded Hsieh Su-wei of Taiwan on Saturday, while Serena Williams was forced to withdraw with a knee injury.