Third seed Maria Sharapova ousted fellow Russian Elena Vesnina 6-4 6-2 despite facing nine break points at the Sony Open in Miami on Sunday.
Sharapova will meet Klara Zakopalova in the fourth round following her 6-2 7-6 (7/4) win over Maria Kirilenko.
Sixth seed Angelique Kerber and 11th seed Nadia Petrova went out, however.
Kerber was thrashed 6-4 6-0 by Sorana Cirstea while Petrova lost 7-6 (9/7) 6-4 to Jelena Jankovic.
Cirstea, who will face Jankovic in the fourth round, said: “I didn’t have any expectations coming into this tournament because I’ve never played that well in Miami.
“But I’ve been fighting the best I could and working my way through every single match, and it’s working. When you work so hard on everything, it’s nice to see the results coming.”
Eighth seed Sara Errani breezed past Simona Halep 6-1 6-0 to secure a last-16 meeting with 12th seed Ana Ivanovic, who overcame two-time major winner Svetlana Kuznetsova 6-3 6-3.
Roberta Vinci, seeded 15, battled from a set down to advance with a 5-7 6-4 6-4 triumph over Carla Suarez-Navarro. The Italian will take on Alize Cornet in round four after the French 32nd seed toppled Lauren Davis 2-6 6-3 6-2.
