Vandeweghe returned in July after a 10-month injury absence, but the two-time grand slam semi-finalist is still looking for top form.
The American has lost three of four matches since making her comeback, the latest of which was a 6-3 6-0 defeat to lucky loser Anna Blinkova at the WTA International event.
Another former grand slam semi-finalist, Petkovic upset fourth seed Zhang Shuai 6-3 6-4 in the first round.
Petkovic will meet Camila Giorgi after the Italian brushed past Margarita Gasparyan 6-3 6-2.
Three seeds – Katerina Siniakova, Aliaksandra Sasnovich and Karolina Muchova – moved through, while Yulia Putintseva joined Zhang in exiting.
Other first-round winners were Fiona Ferro, Mihaela Buzarnescu, Kristie Ahn, Magda Linette and Anastasia Potapova.