It's something incredible for me. It's something that I've been dreaming of all my life, being here and even more so beating the world number one. I'm super, super happy
The 25-year-old clinched her maiden crown at the All England Club by beating Karolina Pliskova 6-3, 6-7 (4/7), 6-3 on Saturday, adding to the French Open title she won in 2019
Thursday's result was almost identical to Pliskova's win over Ostapenko in the 2018 quarter-finals in Stuttgart when the Czech went on to capture the title.
Earlier, Anett Kontaveit of Estonia set up a second-round tie with third-seed Sofia Kenin of the USA after a 6-2, 6-3 win over German qualifier Julia Middendorf.
US teen Coco Gauff booked a quarter-final meeting with Tunisia's Ons Jabeur. Gauff beat compatriot Lauren Davis 6-2, 7-6 (7/2) while Jabeur rallied for a 5-7, 6-3, 6-3 victory over France's Alize Cornet.
Rublev, up 6-1, 5-2, was unable to convert three match points before the players had to leave the court for the second of two rain delays, but he wasted no time in closing out the match when play resumed.
The see-saw continued in the third set with breaks traded before Brady took control of Pegula's serve to reach the final four of a Grand Slam for the second time.