Serbia's Djokovic needed 86 minutes to dispatch Jeremy Chardy of France 6-3, 6-2, 6-2, but fourth-seeded Ferrer of Spain labored through five sets before ousting Alexandr Dolgopolov of the Ukraine.
Ferrer will next face Ivan Dodig of Croatia, who was leading Ivan Sijsling of the Netherlands comfortably when Sijsling called it quits due to an injury.
The Czech Republic's Berdych had to overcome a first-set loss to record a 3-6, 6-3, 6-4, 7-5 win over South Africa's Kevin Anderson. He next faces Australia's Bernard Tomic, who upended No. 9 Richard Gasquet of France 7-6 (9-7), 5-7, 7-5, 7-6 (7-5).
Argentina's Del Potro had little trouble in his 7-5, 7-6 (7-3), 6-0 win over Slovenian Grega Zemlja, and will face Italian Andreas Seppi, who posted a 3-6, 6-2, 6-7 (4-7), 6-1, 6-4 triumph over Japanese 12th seed Kei Nishikori.