The Ukrainian derby, which took place on Rod Laver Arena, ended 6-2, 6-2 in favor of the 23-year-old Svitolina, Ukrinform reports.
The match lasted exactly one hour. Svitolina had five aces, while Kostyuk had nine double faults.
In the fourth round of the first of the four Grand Slam tennis events of the year, Svitolina will take on world No. 130 Denisa Allertova of the Czech Republic, who beat Pole Magda Linette 6-1, 6-4.
Kostyuk has become the youngest tennis player since 1996 to reach the third round at Australian Open.