Rublev next faces top-seeded Rafael Nadal, who beat Alexandr Dolgopolov 6-2, 6-4, 6-1 earlier Monday.
Nadal got to the round of eight in NY for the first time since his 2013 title, overwhelming 64th-ranked Alexandr Dolgopolov 6-2, 6-4, 6-1.
For its part, Vandeweghe reached the quarterfinals of a Grand Slam tournament for a third time this season. We already have confirmation that the women's draw will feature one all-American semi-final - Venus Williams versus the resurgent Sloane Stephens - and today we discover whether it's going to be a clean sweep in the last four.
Pliskova needed just 46 minutes to defeat Brady 6-1, 6-0 inside Arthur Ashe Stadium.
Vandeweghe, the world No 22, is through to her second Grand Slam semi-final of the year following her excellent run at the Australian Open, but this is the first time the 25-year-old has made the last four here. "Sometimes you just need to have some of those matches where you can just really get through it".
"I didn't change anything". I didn't even practice yesterday.More news: Defending champion Kerber beaten by Japanese teenager at US Open
"When I won this event as a junior at 16, I always dreamed about being on the real stage", Vandewedge said.
Vandeweghe had said beforehand that it would be a match of "first-strike" tennis between two of the best servers and biggest hitters in the game, and the American proved the more clinical.
She wouldn't have much problem if she plays as she did in a almost flawless fourth-round performance, looking nothing like the player who almost went home a round earlier.
Meanwhile, Nadal has dropped the first set in each of his last two matches.
After facing a match point during her third-round battle against Zhang Shuai on Saturday (local time), Pliskova was never pushed by Brady this morning, who failed to find her groove on a sunny day that cast a severe shadow across center court.
Vandeweghe took the match in fitting fashion: with her serve.More news: Su'a Cravens: I need to follow 'what makes me happy'
With Wimbledon champion Garbine Muguruza knocked out on Sunday night by Petra Kvitova, this now appears a golden chance for Pliskova to win her maiden grand slam title.
The one-time world number 15 has struggled with injuries in recent years, and is playing in her first Grand Slam proper since 2015.
"I was not playing my best tennis this tournament. I think one of the best, even this year", said Pliskova after reaching her second straight US Open quarterfinal.
"I definitely felt like I hit a wall at the beginning of the second set", Keys said.
In the next round, Kanepi will play against the Ukrainian Elina Svitolina, the American Madison Keys.More news: Dozens detained as Tamil Nadu braces for the next storm ---- Anitha