Rafael Nadal advanced to the fourth round of the Sony Ericsson Open by beating qualifier Frederico Gil 7-5, 6-3.
The top-ranked Nadal struggled with his second serve and was broken twice on Monday but gradually wore down Gil, who is ranked a career-best 74th.
The top men have avoided the wave of upsets that has marked the women's draw. The latest surprise was 18-year-old Caroline Wozniacki's victory over fourth-seeded Elena Dementieva 7-5, 6-4.
Wozniacki, who last week was selected WTA Tour newcomer of the year for 2008, advanced to the quarterfinals. She took advantage of 45 unforced errors by Dementieva.
Wozniacki is the first Danish woman to crack the top 20, reaching a career-high 12th in the rankings while benefiting from recent workouts in Las Vegas with Andre Agassi's former trainer, Gil Reyes.
"It feels amazing to me that I'm the No 12 in the world," Wozniacki said.
Despite a sluggish start and wobbly finish, Venus Williams defeated No 10-seeded Agnieszka Radwanska 4-6, 6-1, 6-4. The three-time champion double-faulted three times in the last game before finishing with an ace.
"Fortunately I've had experiences like that before," Williams said. "I know how to get through it."