The Slovakian was broken five times as Agnes Szavay, ranked 41, clinched a 7-5 6-3 victory in one hour 53 minutes to set up a clash with Alona Bondarenko of Ukraine.
After dropping the first set, world number 10 Hantuchova looked back on track when she recovered from an early break down in the second set.
But the 18-year-old Szavay then broke again and held on for victory.
"I really served good in the first set and my drop shot was also good," Szavay said.
"I just lost to Bondarenko at Wimbledon but I didn't play my best tennis then so I hope it is better this time."
Hantuchova admitted she had not expected Szavay to perform at such a high level.
"I was really surprised the way she played," Hantuchova said.
"She was just better on the day and took her opportunities. I missed so many easy returns and didn't make enough first serves. That was the key today."
Top seed Svetlana Kuznetsova looked set to follow Hantuchova out of the tournament when she trailed Agnieszka Radwanska of Poland 2-0 in the final set of their second-round encounter.
But the Russian won four straight games and held on to win 4-6 6-1 6-4 and seal a quarter-final against Italian Francesca Schiavone, who beat Frenchwoman Emilie Loit 6-1 6-4.
Wimbledon runner-up Marion Bartoli survived a second-set scare to beat Virginia Ruano-Pascual 6-0 6-4 and book a quarter-final place against Russian sixth seed Elena Dementieva, who beat American wildcard Ashley Harkleroad 6-1 7-6.
Fourth seed Dinara Safina advanced but seventh seed Sybille Bammer was beaten 1-6 7-5 6-2 by Eleni Daniilidou of Greece.
In the men's event, top seed Nikolay Davydenko was pushed all the way by American wildcard Donald Young before coming through their second-round match 6-2 4-6 7-5.
The Russian breezed through the first set, but Young, whose opening-round win was his first on the ATP Tour, hit back before Davydenko snatched the final set for victory. The Russian will now play French 13th seed Gilles Simon.
Fourth seed David Ferrer beat John Isner for the second time in a week, downing the American 6-7 6-2 6-2 to reach the third round, where he will play Russian Igor Andreev.
Fifth seed Paul Henri-Mathieu of France beat Peruvian Luis Horna 6-3 7-6 to set up a clash with Spanish 10th seed Nicolas Almagro, who came from behind to beat another Frenchman, Julien Benneteau, 6-7 6-3 6-3.
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