Swiatek got the point and the hold against Kontaveit, but she later blinked to drop the second set.
In the third set, Kontaveit took a 5-1 lead, twice breaking Swiatek, who made less than half of her first serves over the course of the match. Swiatek reeled off four consecutive games to even the score at 5-5, but in the end, Kontaveit, the No. 28 seed at age 24, proved to have steelier nerves in the most important moments.
She took the match, 6-7, (4), 7-5, 7-5, to make her first major quarterfinal, successfully following up on her third-round thrashing of Belinda Bencic. In the quarters, she takes on reigning Wimbledon champion Simona Halep.