Dulko had to play only one game of her match with Jelena Dokic before Dokic retired with an injury. Dulko will likely have to work much harder in her second-round match when she takes on second-seeded Maria Sharapova, who was a finalist at the Australian Open this year.
Sharapova and the other 31 seeded players in this tournament received a bye past the first round.
Irina Falconi moved on when Alexandra Dulgheru retired in the second set. Falconi lost the first set 6-4 but had a 5-2 lead in the second when Dulgheru called a halt to the match.
Falconi will take on sixth-seeded Samantha Stosur in the second round.
Fourth-seeded Caroline Wozniacki will face Ekaterina Makarova in the second round after Makarova got past Bethanie Mattek-Sands 6-2, 6-3.
Other first-round winners Thursday included Varvara Lepchenko, Chanelle Scheepers, Tamira Paszek, Lesia Tsurenko, Sofia Arvidsson and Simona Halep.
The second round begins Friday with world No. 1 Victoria Azarenka meeting Mona Barthel.