With four of the top eight seeds falling in Auckland on Tuesday, the big names left standing made sure they got through safely in the second round.
The second-seeded Ivanovic was perhaps the most impressive, dropping just two games on her way to a 6-1 6-1 win over Johanna Larsson.
At WTA Brisbane, second seed Victoria Azarenka smashes Casey Dellacqua 6-3 6-1 in her first match of the new season.
Third seed Maria Sharapova joined her in the third round without hitting a ball as local hope Ashleigh Barty was forced to pull out of their clash before it started.
2013 Wimbledon finalist Sabine Lisicki, seeded seventh in Brisbane, also fell foul of injury. Her withdrawal put Stefanie Voegele of Switzerland into the third round.