For Stosur, who upset Serena Williams to win her one and only Grand Slam title at the 2011 US Open, it was the same old story at Melbourne Park where she has never surpassed the fourth round and suffers annual bouts of stage-fright.
The muscular 29-year-old threw away a dominant early position and by the third set had stiffened up to the point where her legs almost refused to move.
"It was a match of the highest quality. She is a very tough opponent and I just hung in there," said Ivanovic.
"The conditions were hot and I am very happy and thrilled to get through. Winning in Auckland gave me a lot of confidence and I'm looking forward to the challenge of playing Serena."
Fourth seed Li Na saved a match point before rallying past a combative Lucie Safarova to record a 1-6 7-6 6-3 third round victory in Melbourne.
Li initially appeared out of sorts as the 26-year-old Czech attacked her forehand and serve, resulting in a slew of errors from the Chinese number one, who remained committed to her aggressive style even when she was playing badly.
Safarova, who has never beaten a top-10 opponent in a WTA Tour event, served for the contest in the ninth game of the second set and held a match point in the 12th before Li held, then produced a remarkable tiebreak that she clinched 7-2 to send it into a decider.
"I think the five centimetres saved my tournament," Li said after another long match played in temperatures over 40 degrees Celsius. "If she had hit it in ... the whole team (would have been) on the way to the airport.
"At least I won the match, so I am still in the tournament. I was really happy the way I fought on the court from first point until the last point."
The 2011 French Open champion and Safarova continued to punch and counter punch in an entertaining third set before Li broke in the eighth game and then held serve to set up a fourth round clash with Russia's Ekaterina Makarova.
Makarova eased past Monica Niculesu 6-4 6-4 with a minimum of fuss to book her place in the last 16, where she was joined by 30th seed Eugenie Bouchard. The Canadian reached the second week of a grand slam for the first time in her career with a confident 6-2 6-2 victory over Lauren Davis. Bouchard will next face home favourite Casey Dellacqua after the Australian eased past an unwell Zheng Jie 6-2 6-4.
Flavia Pennetta survived a second set fightback from talented German Mona Barthel to reach the fourth round with a 6-1 7-5 win. Next up for the 28t-seeded Italian will be Germany's Angelique Kerber, who progressed after baeting Alison Riske 6-3 6-4.
Third round results
1-Serena Williams (U.S.) beat 31-Daniela Hantuchova (Slovakia) 6-3 6-3
4-Li Na (China) beat 26-Lucie Safarova (Czech Republic) 1-6 7-6(2) 6-3
9-Angelique Kerber (Germany) beat Alison Riske (U.S.) 6-3 6-4
14-Ana Ivanovic (Serbia) beat 17-Samantha Stosur (Australia) 6-7(8) 6-4 6-2
22-Ekaterina Makarova (Russia) beat Monica Niculescu (Romania) 6-4 6-4
28-Flavia Pennetta (Italy) beat Mona Barthel (Germany) 6-1 7-5
30-Eugenie Bouchard (Canada) beat Lauren Davis (U.S.) 6-2 6-2
Casey Dellacqua (Australia) beat Zheng Jie (China) 6-2 6-4