The British star reached the quarter-finals in Stuttgart, where she was beaten by conqueror Iga Swiatek, and she won her opener in Madrid against Tereza Martincova as she gets used to life without again coach.
It was a slightly uncomfortable opening set for Raducanu, but she then cruised through the second to win 7-6 6-0.
Next up is a familiar enemy in Ukraine, Kostyuk, who is also 19.
The pair met several times as juniors before their first professional encounter late last year at the Transylvania Open. Kostyuk took the win that day, winning 6-2 6-1 in the quarter-finals, and Raducanu will be looking for a much better performance.
“Throughout the juniors she was always the favorite when we played,” Raducanu said ahead of Saturday’s game.
“She was considered much better. Yeah, it’s funny. When we played last year, she played very well, but I wasn’t very well that day either. So it will be an interesting match.
UK start date, location and time
The round of 16 between Emma Raducanu and Marta Kostyuk will take place on Sunday, May 1.
The action is expected to begin around 3:15 p.m. GMT.
Garbine Muguruza or Anhelina Kalinina await the winner in the next round.
How to watch Emma Raducanu vs. Marta Kostyuk
TV channel: The match will be broadcast on the Amazon Prime streaming service.
Direct: Amazon Prime subscribers will be able to watch the game either on their website or through the app.
Summary of the confrontations between Emma Raducanu and Marta Kostyuk
The pair have met once before on the WTA Tour, when Raducanu managed just three matches last October in Romania.
Raducanu wins: 0
Kostuyk wins: 1