She will play the winner of the fourth-round clash between China's Jie Zheng and Italian Sara Errani.
Kvitova, the second seed, whipped through the first set in 31 minutes.
She successfully challenged a ball called out on set point to take out the first.
Kvitova broke serve in the fifth game of the second set but struggled to hold her own serve two games later.
Eventually, the left-hander pushed the Serb out of court and moved to a 5-3 edge with a return down the line.
But Ivanovic battled back, securing a service break of her own to level at 5-5 before moving ahead to 6-5 on serve.
Ivanovic held serve in the following game in comical circumstances when she returned a high ball and Kvitova, waiting at the net, made a fresh-air attempt at a smash.
As the set went to a tiebreak, Kvitova ran up five match points and, while Ivanovic saved one, she surrendered on the second with a return dumped into the net.
In the men's draw Britain's Andy Murray needed only to appear on court at Rod Laver Arena to make it into his fifth successive grand slam quarter-final.
Murray, the fourth seed, took the first two sets from Mikhail Kukushkin of Kazakhstan 6-1 6-1 before his opponent withdrew from the match with a hip injury after losing the first game of the third set.
Kukushkin was clearly troubled by the problem throughout their fourth round match.
He offered only token resistance to Murray after previously playing one of the most entertaining matches of the championship to beat Frenchman Gael Monfils in five sets.
For Murray the win put him one match closer to the grand slam title he has come so close to on three occasions.
The runner-up at the past two Australian Opens, Murray was also a beaten finalist at the 2008 US Open.
He was also a semi-finalist in the final three grand slams of 2011.
- AAP
