The meeting lasted 2 hours 34 minutes and ended with a score of 5: 7, 6: 4, 6: 4 in favor of the 130th racket of the world.
Svitolina is ranked 15th in the WTA rankings and is the champion of the 2018 Final Tournament.
In the next round, Hasanova will play against the Japanese Misaki Doi, who defeated Kristina Kuchova from Slovakia.
Earlier it was reported that Russian Ekaterina Aleksandrova lost to Canadian Leila Fernandez at the start of the tournament in Adelaide.