The Serb looked to be heading for an early exit from the Australian Open warm-up event when she trailed 5-2 in the deciding set before reeling off five games to join Slovenian Katarina Srebotnik in the quarter-finals.
Ivanovic, ranked four in the world, said she had trained harder than ever over the summer and her confidence was soaring ahead of the first grand slam of the year.
"This match today gives me some confidence because I am coming into the new season looking for some tough matches and to get through them," she told a news conference.
"There are many opponents and players who want exactly the same thing, but I think I have a game that can get me to win a grand slam."
Ivanovic is on course for a semi-final meeting with Justine Henin after the world number one strolled into the quarters without hitting a ball when her opponent, Czech Lucie Safarova, withdrew with a buttock strain.
Russia's U.S. Open finalist, second-seed Svetlana Kusnetsova, also eased into the next round with a comfortable 6-3 6-4 win over Israel's Shahar Peer.
Third-seeded Serb Jelena Jankovic showed no ill-effects from the leg injury that forced her to forfeit her singles match in last week's Hopman Cup final as she dispatched France's Tatiana Golovin 6-1 2-6 6-3.
While the women's matches mostly went according to the rankings at Sydney's Olympic tennis centre on Tuesday, there was an early upset in the men's draw when Spanish second seed Tommy Robredo was beaten by Czech Radek Stepanek 6-4 6-2.
Carlos Moya kept the Spanish flag flying with his 1-6 6-4 6-2 victory over Austrian Stefan Koubek to stay on course for a possible semi-final with Australia's Lleyton Hewitt, who is chasing a record fifth title in Sydney.
Hewitt beat Frenchman Nicolas Mahut 6-3 6-4 to set up a second round meeting with his Davis Cup team mate Chris Guccione. (Editing by John O'Brien)
