The Serbian triumphed at the WTA International event in 2008 and 2010, but missed the chance to secure a third last year when she was beaten in the final by Angelique Kerber.
Ivanovic has won four titles on the Tour so far this year and has reached the semi-finals in three of her last five hard-court events.
She cruised past the world number 75 on Tuesday with a 6-3 6-2 victory to book her place in the second round.
After losing on her own serve in the opening game, Ivanovic bounced back with two breaks of her own to claim the first set.
Once the opener had been secured, the 26-year-old finished with a flourish in the second - winning five games in a row to to seal her progression.
Seventh seed Karolina Pliskova also had no problems getting past first-round opponent Kirsten Flipkens, winning 6-2 6-4, but Andrea Petkovic suffered a surprise defeat at the hands of Camila Giorgi.
Petkovic's serve started well but, from the fourth game of the opening set, she only held twice as Giorgi recorded a 6-1 6-2 win - her third against the German.
Giorgi was dominant on her own serve and converted four of her five break points against the fourth seed to set up a second-round match with Ons Jabeur, who beat Donna Vekic 7-5 6-1.
There were also straight-sets victories for Mona Barthel - 6-3 6-1 against Kiki Bertens - and Tsvetana Pironkova, who beat Lisa-Maria Moser 6-2 6-3 in 63 minutes.
Jana Cepelova had a tougher day in Austria as she was taken to three sets by Timea Bacsinszky, the Slovakian eventually winning 7-6 (7-3) 1-6 6-4.
Klara Koukalova also failed to put her match with Katerina Siniakova to bed in two sets, but eventually booked a second-round tie with Marina Erakovic in a 7-5 3-6 7-6 (7-3) win.
Qualifier Madison Brengle will meet Ivanovic in the next round after Irina-Camelia Begu retired through injury with the American 7-5 3-1 up, and Magdalena Rybarikova came through 6-4 5-7 6-2 against Kaia Kanepi.