The Danish second seed fell to Kiki Bertens 6-2 6-2 in the third round.
Bertens, who reached the 2016 French Open semi-finals, beat the 27-year-old Dane 6-2 6-2 in an hour to claim the biggest scalp of her career.
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Australian Open champion Wozniacki had to win the Madrid title to overhaul Simona Halep in the top spot but her defeat means the Romanian will retain first place.
Bertens' will face five-time grand slam champion Maria Sharapova or Kristina Mladenovic of France in the last eight.
Earlier on Wednesday Simona Halep made it six sets without reply after cruising past Kristyna Pliskova 6-1 6-4.
Halep, the two-time defending champion, struck 20 winners and broke Pliskova's serve three times as she extended her winning streak in the Spanish capital to 15 straight matches.
After conceding the opener in 29 minutes, Pliskova produced a better second set but failed to deliver consistently as Halep saved all five of the break points she faced.
"I think she served much better (in the second set) and I couldn't do much with the return," Halep told a news conference.
"But I served well, too. I feel like it was a very good match, the hardest here. She has improved a lot since last year, we played together here, and she was a different player."
Halep will next face Kristyna's twin sister Karolina Pliskova, who raced past American Sloane Stephens 6-2 6-3.
Svitolina - Halep - US Open Highlights
Svitolina downs Halep to reach US Open quarter-finals