The Spaniard crumpled in the third set as 100th-ranked Vickery clinched the biggest win of her young career.
"I've just worked so hard for so many years and I've always been so close but just could never really get over that hump," 22-year-old Vickery said in an on-court interview.
"This is just the most amazing night of my life and I couldn't be happier.
"Honestly I couldn't believe it. I just tried to fight every point and just hang in there. The crowd was amazing and got behind me."
Earlier, Petra Kvitova survived a marathon match against Dulia Putintseva of Kazakhstan to emerge with a 6-7(4) 7-6(3) 6-4 win.
After capturing her 21st and 22nd career titles in St. Petersburg and Doha, ninth seed Kvitova was not at her best, mixing 66 winners with 78 unforced errors.
The twice Wimbledon champion finally triumphed in three hours and 17 minutes as a frustrated Putintseva smashed her racket on the court after coming so close to an upset.
"It’s kind of tough to explain, because it was really up-and-down," Kvitova told reporters after her 14th straight victory, matching the longest steak of her career.
"My mental side wasn’t really tough, I have to say. It was always, like, a good point and I was up mentally, and then it was a bad point, and I was down. That was almost all match.
"I couldn’t show the game which I played the last few weeks."
Next up for Kvitova will be 16-year-old American wild card Amanda Anisimova, who dominated Russian 23rd seed Anastasia Pavlyuchenkova 6-4 6-1.
Anisimova, the U.S. Open junior champion, ended the match with an audacious and perfectly executed drop shot.
Romanian top seed Simona Halep used a superior serve to beat Czech Kristyna Pliskova 6-4 6-4 on a day when nine seeds were beaten, including Agnieszka Radwanska (31).
Radwanska was beaten by Japan's Naomi Osaka, who continued her barnstorming form with a 6-3 6-2 victory two days after ousting former world number one Maria Sharapova.
Osaka, 20, dominated on first serve, and also broke four times.
Her next opponent will be Vickery.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford/Amlan Chakraborty)
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