Flipkens had a career-best Grand Slam result in getting to the semis at the All-England Club this summer. But she hit a rough patch after that, in fact losing six of seven matches coming into Linz.
However, the fifth-seeded Flipkens showed off her Wimbledon form by converting on five of six break point chances and saving all three of the ones on her own serve in her 62 61 second round victory over the Italian qualifier Giorgi.
"The score doesn't say everything today," Flipkens said. "It was 62 61, but it was more of a battle than the score said. She's a good player. She came out of qualies, so you know you have to watch out for those players. She's an up-and-coming talent. She plays so aggressively. I was really lucky that I served well today and that my slice was doing its job."
Another second round match saw third-seeded Ana Ivanovic beat Francesca Schiavone, 63 75, in a clash featuring former French Open champions. Ivanovic improved to 5-0 in her series with Schiavone while clinching a quarterfinal berth for the sixth time in six appearances in Linz.
Top-seeded Angelique Kerber got her Linz campaign started with a forgettable first set, but turned it around quickly for an 06 61 62 triumph over Romania's Monica Niculescu. Her 40th match win of the year set up a second round encounter with another Romanian, Alexandra Cadantu.
"In the first set I wasn't there," Kerber said. "I was a little bit nervous. But after that, I got my rhythm and tried to fight until the last point and have fun. I'm just happy to have won such an up-and-down match."
"I had some problems with my foot in Beijing and had to rest for quite some time afterward, so I didn't expect much today," Hantuchova said. "But I tried my best and she was playing too well. I felt like I was starting to play much better in the second set, but unfortunately I didn't take advantage of my chances."