Top seed Serena Williams set a new record en route to the Australian Open fourth round Friday as Li Na avoided an upset by fighting back from match point to stay alive. On another hot Melbourne day, the world number one and five- time tournament champion powered past Daniela Hantuchova 6-3, 6-3 to record her 61st Australian Open win, surpassing the previous mark set by Margaret Court. Asked which had been her favourite matches, Williams, who made her Melbourne debut as a 16-year-old in 1998, replied: “All the finals I was able to win.” Few are betting against the American adding a sixth Australian title after another sublime performance from a player who is gunning to match the achievement of Chris Evert and Martina Navratilova in winning her 18th Grand Slam. She used her powerful serve to help dull the challenge from the experienced Slovak to set up a fourth round clash with either former world number one Ana Ivanovic or 2011 US Open champion Samantha Stosur. “I feel good to have gotten through that one because it was tough conditions out there,” she said, referring to temperatures which were already at 36 Celsius (96.8 Fahrenheit) at the 11:00 am start. Williams, who has lost just 12 games in her three matches so far, added that she needed to lift her game further against Stosur or Ivanovic. “If I don’t, I won’t be in the tournament much longer.” Chinese fourth seed Li is fortunate to still be in contention after surviving an onslaught by Czech Lucie Safarova. Li, who lost in the final to Victoria Azarenka last year, self-destructed in the first set and had to draw on all her experience to find a way past the 26th seed. In doing so, she saved a match point in the second set and then battled through a tiebreak before winning 1-6, 7-6 (7/2), 6- 3 in a two-and-a-half hour marathon.