Caroline Wozniacki eliminated eighth-seeded American Madison Keys and Angelique Kerber took care of two-time Wimbledon champ Petra Kvitova as half of the women's quarterfinal draw was set at the US Open during Sunday play.
Wozniacki's 6-3, 6-4 win over Keys stretched her deepest run at a Grand Slam tournament in two years.
Wozniacki is a two-time runner-up at Flushing Meadows, but she is unseeded and ranked only 74th after a season filled with injuries and poor results.
"I know it sounds bad, but honestly, at this point I'm like, I really don't care what my ranking is," Wozniacki said. "Because if I'm not in the top five, I feel like it's not where I want to be, so at that point, whether I'm 20 in the world or 100 in the world, it doesn't matter because I'm going to play the same people anyway.
"The main thing is that when I'm on court I have to believe in myself. That's what I care about, that I know that I can do it. I know I can beat anyone. I think it just sucks for some of the other players who have to play me early."
With Kerber making the quarters, Williams will need to advance to the final to retain the No. 1 ranking.
On Sunday, Wozniacki made only seven unforced errors, 26 fewer than Keys.
Wozniacki will next play Anastasija Sevastova, who posted her second big upset of the tournament by beating 13th-seeded Johanna Konta 6-4, 7-5 to become the first Latvian woman to make the final eight at a Grand Slam since Larisa Savchenko in 1994.
"I still cannot believe it," she said. "Mentally I'm spent. Totally spent. But it's amazing."
Sevastova's previous best showing at a major was the round of 16 in the 2011 Australian Open. But after a series of injuries that drained the fun out of tennis, she retired in 2013.
During her break of nearly two years, Sevastova took classes in Austria in "leisure management" -- studying accounting and marketing in hopes of perhaps going into sports management.
When her health improved, she came out of retirement at the start of last season, never expecting she'd be making a deep run at a Grand Slam so soon.
She's more mature, both mentally and physically, Sevastova said. And it also helped that "I saw that there is life without tennis."
As in her second-round upset of third-seeded Garbine Muguruza, Sevastova wobbled under the pressure at first, failing to serve out the match. But as in that victory over the French Open champ, she finally closed out the win with a service break.
Sevastova broke Konta seven times in 11 service games.
"In the end I just stop thinking and I just try to play tennis," Sevastova said.
In the evening match, Angelique Kerber beat two-time Wimbledon champ Petra Kvitova 6-3, 7-5.
Kerber, the tournament's second-seeded player, was content to run Kvitova around the court and wait for her to make mistakes.
The Australian Open champ had only eight winners, but that was just fine in light of Kvitova's 43 unforced errors. She also had seven double faults -- the last on match point.
Kerber will face off against seventh-seeded Roberta Vinci, last year's US Open runner-up, who beat 99th-ranked Lesia Tsurenko 7-6 (5), 6-2.
Vinci has never reached the quarters at any of the other three Grand Slams, but she has now done it four times at Flushing Meadows.
She made her first major final here last year at age 32, stunning Serena Williams in the semis to thwart the American's Grand Slam bid.
Vinci has been bothered by an injured left Achilles tendon and struggled physically at times Sunday.
Exhausted after the match, she had tears in her eyes. The 27-year-old Tsurenko had never been past the third round at a major before this tournament.
Information from The Associated Press was used in this report.