Swiatek is the only top-10 player in the last eight of the women's draw at Roland Garros after beating the 18-year-old Kostyuk 6-3 6-4 on Monday.
Playing her first night match on Court Philippe-Chatrier, Swiatek came from a break down in a thrilling first set and went on to book a meeting with Maria Sakkari – conqueror of last year's runner-up Sofia Kenin.
Eighth seed Swiatek has won 22 consecutive sets at the Paris grand slam and is a strong favourite to win back-to-back titles.
Swiatek, who won a marathon doubles match in combination with Bethanie Mattek-Sands on Sunday, was 2-1 down in the opening set as world number 81 Kostyuk was rewarded for her positive approach.
The 20-year-old Pole responded like a champion, though, breaking back immediately and again after fending off two break points to take a 4-3 lead.
Swiatek, demonstrating her great power and precision, served out the opening set and went a break up at 2-1 in the second, but Kostyuk – playing at this stage of a grand slam for the first time –was not finished yet.
The teenager defended brilliantly and showed great speed over the court as she broke back to level at 2-2 when Swiatek netted a backhand.
Yet Swiatek edged back in front when Kostyuk put a backhand of her own into the net and sealed victory with a magnificent winner – her 24th of an entertaining match.