The 22-year-old, who reached the second round of the Brisbane International after coming through qualifying, beat France's Chloe Paquet 6-3 4-6 6-2.

She was the only British winner in Melbourne after Naomi Broady and Gabriella Taylor lost their matches.

World number 132 Dart will next play Xu Shilin of China as she seeks to qualify in Melbourne for the first time.

Dart will need to win three matches to reach the main draw of the Australian Open, which begins on 14 January.

Taylor lost the first four games of the match as she was beaten 6-1 6-1 by American Kristie Ahn in just 65 minutes.

British number seven Broady lost 6-4 3-6 6-3 to Ysaline Bonaventure of Belgium.

Dan Evans, Jay Clarke, James Ward and Katie Swan begin their qualifying campaigns on Wednesday.

Elsewhere, Sloane Stephens came within two points of defeat in her first-round match against qualifier Ekaterina Alexandrova at the Sydney International.

Stephens, the American world number five, eventually prevailed 0-6 7-6 (7-3) 7-6 (7-3).

Czech Petra Kvitova beat Belarusian Aryna Sabalenka 6-1 7-5, while defending champion Angelique Kerber of Germany overcame Italy's Camila Giorgi 7-6 (7-3) 6-2.

However, former world number one Garbine Muguruza was forced to withdraw from the tournament - the final WTA event before the Australian Open - with illness.