Kostyuk entered the tournament ranked No. 521 - a number that will likely be halved next month - and had wins over 25th-seeded Peng Shuai and Olivia Rogowska to become the youngest player to win main-draw matches at the Australian Open since Martina Hingis in 1996.
Svitolina will now face Denisa Allertova in the fourth-round.
Caroline Wozniacki, seeded second, battled her temper late into the match as she beat Kiki Bertens in the third round of the Australian Open on Friday.
"She's a great player, but what I learned is that you can play against everyone".
"It was sad playing another Ukrainian girl", said Svitolina.
The Ukrainian conceded only her second set in seven matches this year but ultimately found a way past her Czech opponent 4-6, 6-2, 6-1 as the temperatures soared on Rod Laver Arena.
"Well, because I know that I could play much better".
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The 14th seeds had a tougher time, rallying from a set down to overcome Michaella Krajicek of the Netherlands and Alla Kudryavtseva of Russian Federation 4-6, 6-3, 7-6 (7/2) in two hours, 24 minutes on Court 13.
Kostyuk's success, coming through qualifying and reaching the third round, has been one of the stories of the tournament but she found Svitolina too strong and too experienced in her debut on Rod Laver Arena. No. 10 Pablo Carreno Busta beat No. 23 Gilles Muller and will next play No. 6 Marin Cilic, a 7-6 (4), 6-3, 7-6 (4) victor over Ryan Harrison.
"How much you have to pay Svitolina to have one-hour lesson - I got it for free".
Spaniard Rafael Nadal on Friday thrashed Damir Dzumhur of Bosnia 6-1, 6-3, 6-1 to book a place in the fourth round at the Australian Open tennis tournament for the 11th time in his career.
While admitting she was overawed by the occasion at Melbourne Park, teenage sensation Marta Kostyuk showed she can match it with the best following her Australian Open exit.
Thai qualifier Luksika Kumkhum produced a gritty display against Petra Martic, yet it was the Croatian who came through in three sets 6-3, 3-6, 7-5. "You need to be mentally tough and ready to just suffer out there".