Five-time champion Serena Williams rolled to a third-round victory on Saturday, while fourth-seeded Agnieszka Radwanska survived a scare in her third-round match at the Sony Open.
The world No. 1 Williams smashed seven aces en route to a 6-3, 6-3 victory over Ayumi Morita of Japan at Crandon Park.
Next up for the top-seeded Williams will be 13th-seeded Slovak Dominika Cibulkova, who breezed past Romina Oprandi 6-3, 6-4 on Saturday.
The reigning Miami champion Radwanska was pushed to the limit by Slovak Magdalena Rybarikova, but the world No. 4 Pole hung on for a 7-6 (7-5), 2-6, 6-3 victory.
Radwanska will take on 16th-seeded Sloane Stephens in the quarterfinals after the upstart American advanced when former world No. 1 and seven-time major champion Venus Williams withdrew due to a lower back injury shortly before their third-round matchup.
Fifth-seeded Li Na, meanwhile, needed 78 minutes in a 6-2, 6-4 victory over American Varvara Lepchenko. She broke serve four times and had her serve broken just once.
Li, who won the season opener in Shenzhen before finishing as the runner-up to Victoria Azarenka at the Australian Open, will next face Garbine Muguruza after the Spanish wild card upended ninth-seeded Caroline Wozniacki of Denmark, 6-2, 6-4.
Seventh-seeded Czech Petra Kvitova also slipped up on Saturday, as 30th-seeded Belgian Kirsten Flipkens knocked off the former Wimbledon champ 6-0, 4-6, 6-1.
Flipkens will next face Croatian wild card Ajla Tomljanovic, who fought off fellow wild card Andrea Petkovic of Germany, 0-6, 6-4, 7-6 (7-1).