Wozniacki struggled a bit in her opener against Urszula Radwanska but had no such trouble in her 62 61 defeat of the Frenchwoman Parmentier.
"I got more used to the surface compared to the last match and that was definitely a difference," said Wozniacki, who plays Alizé Cornet in the quarterfinals. "It was a very different match compared to the last one."
Wozniacki is now 12-0 here and has won 17 straight sets, the second set of her 2010 semifinal triumph over Anna Chakvetadze being the last one she lost. The only event in which she has a greater winning streak is New Haven, where she has been victorious in 17 straight matches en route to four titles.
"I just enjoy playing in front of the Danish crowd and I'm looking forward to the next match tomorrow," Wozniacki said. "I don't know if I'm the favorite. There are many good players in the draw, and I prefer to take it one match at a time."
No.2 seed Angelique Kerber had a much tougher path to the quarterfinals, beating Anne Keothavong, 46 63 63. She is now 5-1 all-time against Keothavong and 12-3 in her last 15 WTA matches. Next up for her is another German having a career year - Mona Barthel.
Third-seeded Jelena Jankovic also moved on, 63 61, only losing one more game the rest of the way after a 3-3 start to the first set.
"I think I played really well today," Jankovic said. "It was not an easy match, and I'm very happy to be through to the next round. I felt good on the court and it was nice to be hitting the ball well."
Fellow Serb Bojana Jovanovski pulled off the day's lone upset, defeating No.4 seed Monica Niculescu, 67(6) 64 61. Jovanovski had four set points in the first set, including three at 6-3 in the tie-break, but put that disappointment behind her by securing early breaks in the second and third sets.
"I'm so tired now. It was a very tough match, but I´m so happy to have won," said Jovanovski, who is through to her first quarterfinal since College Park last July. "Niculescu is a tough opponent, but I'm very happy with the way I played in reaching the quarterfinals."