Serena Williams survives Sony Open challenge, reaches Miami quarters America's Serena Williams in action against Poland's Caroline Wozniacki in the Women's Tennis Quarter-Final at the London 2012 Summer Olympics on August 02, 2012 in Wimbledon, London. MIAMI, March 25 (UPI) -- Five-time champion Serena Williams barely avoided a fourth-round upset Monday at the Sony Open, rallying to overcome Slovak Dominika Cibulkova in three sets. The top-ranked American needed 1 hour, 57 minutes to mount a second-set comeback and scrape her way to a 2-6, 6-4, 6-2 defeat of Cibulkova and a berth in the Miami quarterfinals. Williams trailed 1-4 in the middle frame but recovered to sweep its final five games, later grabbing the advantage by breaking serve at love for a 2-1 lead in the final stanza. She fired 14 aces, including one to end the match. Williams drew Li Na as a quarterfinal opponent after the fifth-seeded Chinese star advanced with a 7-6 (8-6), 6-2 victory over Spaniard Garbine Muguruza. Also Monday, No. 4 seed and defending champion Agnieszka Radwanska gained the quarters with a 4-6, 6-2, 6-0 comeback win over 16th-seeded American Sloane Stephens. 30 Kirsten Flipkens of Belgium also moved on, rallying over Croat Ajla Tomljanovic 6-7 (6-8), 6-4, 6-3.