By Greg Stutchbury
The Argentine had never advanced past the second round at Melbourne Park in six previous attempts.
Ivanovic has won just one tournament since her breakthrough grand slam victory in Paris, a Tier II event at Linz in 2008, and has failed to make it past the fourth round at any of the grand slams.
Ivanovic admitted she felt her brain was getting in the way of her game and she was overthinking situations when she was playing well, instead of allowing her instincts to take over.
"I start well and I play good, and then, because I have no expectation, I just go out there to enjoy," she told reporters.
"Then I think 'I can play like this all the time' (and) then I get tense and I start making mistakes because I want to play like that (consistently).
"I just have to get rid of that a little bit and just try to play consistent all the time. It might not be at the highest level, but (I have to) just build on it.
"I think when I actually let go of (my) emotions ... that's when I play my best."
Against Dulko, Ivanovic appeared to have given the match away in the final set. An attempted drop shot at 0-15 in the sixth game hit the tape and her shoulders slumped.
Dulko broke to give her the chance to serve for the match, but the Serb managed to find the heart to fight back, reeling off the next three games that had local fans on Margaret Court Arena on their feet cheering on "Aussie Ana."
The courageous display, however, ended in the next game when she gifted Dulko three match points, which the Argentine squandered, before she made no mistake on the fourth opportunity with a forehand service return Ivanovic was unable to retrieve.
"I was really disappointed to fight back in the third set and then make a couple of double faults and basically hand her three match points, then having to fight back," Ivanovic said.
"(But) I feel I have the right things in place and I'm playing, like I said, striking the ball really well.
"That's why it's disappointing when I get on a court and I put so much pressure on myself that it's not enjoyable anymore, it's overwhelming."
(Editing by Patrick Johnston)