The world's 12th-ranked player took advantage of Razzano's late errors for two late breaks at Sawgrass Country Club.
Razzano led 40-0 on serve in the eighth game when Wozniacki reeled off five straight points to break for 5-3 then hold for the first set.
In the second, Razzano again missed game points serving at 5-5 and was broken. Wozniacki won the last game in five points when the 41st-ranked Frenchwoman hit a return long.
"I fought back and played some good points,'' the 18-year-old Wozniacki said. "And, I got a little lucky.''
She said a new conditioning regimen was paying dividends.
"I could see she was getting a little tired,'' Wozniacki said. "I felt good all the way.''
Wozniacki's sixth quarterfinal in seven tournaments this year will be against Slovakia's Daniela Hantuchova, who beat No. 8 Bethanie Mattek-Sands of the United States 6-3, 7-5 in the late match.
"I was really focused the first set and worked well,'' Hantuchova said. "Then she went for some flashy shots and made them. But, I'm really happy with the way I'm playing on clay.''
Fifth-seeded Aleksandra Wozniak of Canada fought off Germany's Sabine Lisicki to win 3-6, 7-6 (3), 6-4 and claim consecutive matches for the first time this year. Next up will be Austria's Tamira Paszek, who reached her first tour quarterfinals since September with a 3-6, 6-3, 6-4 win over Varvara Lepchenko of the United States, who replaced a fatigued Jelena Dokic in the draw.
The top-seeded doubles team of American Lisa Raymond and Kveta Peschke will meet Wozniacki and Strycova in the semifinals. Raymond and Peschke beat American Carly Gullickson and Taiwan's Chin-Wei Chan 6-0, 7-5.
The second-seeds, China's Shuai Peng and Zi Yan lost to American Angela Haynes and Liga Dekmeijere 7-6 (3), 6-4.
Petrova beats 14-year-old Keys at Ponte Vedra
