Petkovic, No. 43 in the rankings, had three third-set breaks to complete the 6-4, 2-6, 6-4 win over Azarenka. Petkovic claimed the only break of the first set but Azarenka was able to even the match with three breaks in the second set.
Petkovic responded with three breaks in five chances in the third set, winning 54 percent of the points off Azarenka's serve.
It was the third consecutive loss for Azarenka, who has dropped just seven matches all year. She was beaten by Serena Williams in the U.S. Open final and dropped a second- round match to Venus Williams last week in Tokyo (Azarenka had a first-round bye) before meeting Petkovic.
Fifth-seeded Sara Errani advanced to the third round with a 6-3, 6-2 decision over Misaki Doi. Errani piled up seven points in nine receiving games.
Lucie Safarova dropped her serve just once in a 6-3, 6-3 win over Kaia Kanepi in another second-round match.
No. 8-seeded Jelena Jankovic and 14th-seeded Ana Ivanovic also won Monday as the first round was completed. Jankovic lost just 14 points in the third set of a 1-6, 6-4, 6-0 win over Anastasia Pavlyuchenkova and Ivanovic took out Flavia Pennetta 7-6 (11-9), 6-1 with five breaks in 10 receiving games.
Svetlana Kuznetsova posted a 6-1, 6-1 rout of Hsieh Su-Wei while Eugenie Bouchard stopped Magdalena Rybarikova 6-4, 6-1. Also Monday, Polona Hercog beat Monica Puig 6-1, 6-4 and Galina Voskoboeva ousted Sharon Fichman 6-4, 6-3.