The former world number one broke Wickmayer five times to book a second-round meeting with former French Open champion Francesca Schiavone.
Second see Sloane Stephens joined Ivanovic in the next round after the American beat Magdalena Rybarikova 6-3 6-1 in the evening match on centre court.
The major upset of the day occurred in the match before Stephens stepped onto court as sixth seed Sorana Cirstea slumped to a 1-6 6-3 6-4 loss to wildcard entrant and local hopeful Patricia Mayr-Achleitner.
It was otherwise a good day for the seeded players as Carla Suarez Navarro, Kirsten Flipkens and Dominika Cibulkova all progressed.
Suarez Navarro was too strong for Kristyna Pliskova, winning 6-2 6-3, although Flipkens and Cibulkova both needed three sets.
Fifth seed Flipkens eventually overcame Donna Vekic 2-6 6-2 6-2 while Cibulkova was a 3-6 6-2 6-1 winner against Annika Beck.
Andrea Petkovic will meet Stephens in the second round after the German won 6-3 7-5 over Yvonne Meusburger.
Camila Giorgi, Katarzyna Piter and Maryna Zanevska also won through.