Simona Halep moved closer to regaining the world number one ranking by coming from a set down to beat Polona Hercog 5-7 7-6 (7-1) 6-2 at the Miami Open.
The 27-year-old world number three lost her place at the top of the women's game following Naomi Osaka's Australian Open victory in January.
But after Osaka's shock exit in the third round in Miami, Halep can return to the top if she takes the title.
She next faces Venus Williams, who swept past 14th seed Daria Kasatkina.
American seven-time Grand Slam champion Williams beat the 21-year-old Russian 6-3 6-1 in just under 75 minutes on Sunday to reach the fourth round.
At number 43 in the world rankings, three-time Miami Open champion Williams, 38, is ranked 21 places lower than Kasatkina.
Romanian Halep, the 2018 French Open champion, arrived in Miami having failed to get past the last 16 in Indian Wells and the quarter-finals in Dubai.
She will also go top of the rankings if she reaches the final and loses to anyone other than Czech world number two Petra Kvitova. Kvitova faces France's Caroline Garcia in the fourth round.
It took her nearly three hours to beat 28-year-old Hercog, the world number 93 from Slovenia.
"She played unbelievable and it was such a tough match," said Halep. "It was good to play for almost three hours though. I slowly found my rhythm but I always had belief so if I can keep doing this, I will have a good tournament."
World number one Osaka was beaten by 27th-seeded Hsieh Su-wei of Taiwan on Saturday, while Serena Williams was forced to withdraw with a knee injury.