Ivanovic needed just under 73 minutes to dispatch the 25-year-old Petkovic, who is struggling to regain her form after injury setbacks.
The eighth-seeded Nadia Petrova of Russia avoided an upset by beating 21-year-old Dinah Pfizenmaier of Germany 7-6 (7/2), 6-4. Mirjana Lucic-Baroni of Croatia defeated another Russian, Elena Vesnina, 6-0, 6-4.
Germany's Sabine Lisicki was playing Nastassja Burnett of Italy in the late match.
Results from day two of the WTA Stuttgart tournament on Tuesday (x denotes seeding):
Women's singles
First round
Sabine Lisicki (GER) bt Nastassja Burnett (ITA) 6-3, 6-4
Ana Ivanovic (SRB) bt Andrea Petkovic (GER) 6-3, 6-2
Nadia Petrova (RUS x8) bt Dinah Pfizenmaier (GER) 7-6 (7/2), 6-4
Mirjana Lucic (CRO) bt Elena Vesnina (RUS) 6-0, 6-4