Former world number one Wozniacki, the runner-up in 2009 and 2014, downed American eighth seed Madison Keys 6-3, 6-4 to make the last-eight in New York for a fifth time yesterday.
Now ranked at 74 in the world after a right ankle injury sidelined her for almost three months, the Danish star hit just seven unforced errors in her win over Keys.
Wozniacki is back in the last-eight of a Slam for the first time since making the semi-finals in New York in 2014.
"I was nervous in the last game. I told my serve please hold out. I knew Madison wouldn't give much up and that she'd go for the big shots, so I tried to keep it on her backhand side."
Sevastova became the first Latvian woman in 22 years to reach a Grand Slam quarter-final when she beat British 13th seed Johanna Konta 6-4, 7-5.
The Briton was undone by 34 unforced errors.
Larisa Savchenko was the last Latvian woman to make the quarter-finals of a Slam at Wimbledon in 1994.
- Latvian breakthrough -
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Sevastova had not won a match in New York since 2010 before this year and with her career unravelling she quit in May 2013 to study leisure management in Austria.
"I had a lot of injuries. I was depressed and it just wasn't fun anymore, but now I'm back," said Sevastova when asked why she turned her back on the sport.
Konta, bidding to become the first British woman in the quarter-finals in New York since Jo Durie in 1983, never recovered from a poor start.
A semi-finalist at the Australian Open in January, the 25-year-old was 3-0 down in the first set and 4-1 behind in the second.
"I just told myself to fight and fight."
Wozniacki defeated Sevastova in their only previous meeting, in straight sets in the Australian Open last 16 in 2011.
Italian seventh seed and 2015 runner-up Roberta Vinci reached the quarter-finals for the fourth time with a 7-6 (7/5), 6-2 win over Lesia Tsurenko of Ukraine.
Vinci, 33, and suffering with a tendon injury in her leg, will face either second seeded Angelique Kerber of Germany or Petra Kvitova of the Czech Republic for a place in the semi-finals.
The remaining four last-16 matches take place on Monday when world number one and six-time winner Serena Williams tackles Yaroslava Shvedova of Kazakhstan.
Carla Suarez Navarro meets Simona Halep while Agnieszka Radwanska takes on teenager Ana Konjuh and two-time champion Venus Williams faces Karolina Pliskova.
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