Ostapenko needed eight match points to get over the line against Svitolina, as the 13th seed continued to back up her remarkable Roland Garros triumph.
Muguruza rallied past Angelique Kerber, 4-6, 6-4, 6-4, and earned a bout with 32-year-old Svetlana Kuznetsova, the first entry into the quarterfinals with her 6-4, 6-2 win over fellow veteran Agnieszka Radwanska.
The Latvian suffered a huge wobble in the second set as Svitolina fought back from 5-2 to lead 6-5, but she steadied to break back, force a tie-break and, belatedly, reach the last eight.
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As a result Kerber will now be replaced a No 1 by either Karolina Pliskova or Simona Halep. Azarenka, who gave birth to son Leo in December, was playing in just her second tournament since returning to competition. Konta edged through 7-6 (7/3) 4-6 6-4 against Frenchwoman Caroline Garcia.
The number ten seed is the only previous victor remaining in this year's tournament, although the last of her five titles at the All-England Club came back in 2008.
But it was Venus Williams who was given the pride of place to start proceedings on Centre Court, where she was pitched against an opponent nearly half her age. Rybarikova swept through in straight sets that time, and Vandeweghe is not daring to think about winning the title despite being tipped by many as a serious contender. "I didn't watch any of the French when I was finished with it", Williams said.
"It's obviously an fantastic feeling for me", she said. "Now it's happening. I would never say it could happen".