The Serbian former world number one, now ranked 16th, needed just over an hour and a half to oust the Italian.
Third seed Ivanovic won the WTA Linz tournament in 2008 and 2010 and will face the winner of Katarzyna Piter and Dominika Cibulkova’s second-round match.
Spain’s Carla Suarez Navarro, the fourth seed, beat Ukrainian Elina Svitolina 6-1 6-4 while fifth-seeded Wimbledon semi-finalist Kirsten Flipkens ousted Camila Giorgi 6-2 6-1.
"The score doesn't say everything today," Flipkens said. "It was 6-2 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."
Suarez Navarro and Belgian Flipkens will face each other in the quarter-finals on Friday.
Delayed first-round matches saw Karin Knapp of Italy beat eighth-seeded 2007 winner Daniela Hantuchova of Slovakia 6-2 7-6(6), while Romanian Alexandra Cadantu knocked out Austrian wildcard Melanie Klaffner 7-6(4) 6-2.
"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."
Knapp will face Switzerland’s Stefanie Voegele in the last 16, while Cadantu plays Angelique Kerber after she beat Romania's Monica Nicolescu 0-6 6-1 6-2.