The number eight seed, looked like she was cruising towards an easy win after storming the first set.
But 17-year-old Hantuchova had other ideas and hit back to take advantage of the Russian teenager's lapse of concentration in the second round.
Kournikova found herself in trouble at 3-0 and then 4-1 down before finally pulling herself together to win the second 7-5.
"After I won that first set pretty easy I kind of relaxed and started to make a few more mistakes," she said.
"But then I found my rhythm again and played well. It was really good for me to fight and that I didn't give away that second set."
Eye-catching
In the first round clash, Kournikova wore a bright yellow, sleeveless top, matching shoes and black shorts which attracted the usual hordes of photographers.
The tennis pin-up revealed that she had helped design her latest outfit, provided for her by sportswear giant Adidas.
"I've always liked fashion and I've always been artistic," she said.
"I've got a great relationship with Adidas - they've always asked my opinion and listened to me.
"I've worn this style of outfit before but the colours are new."
Kournikova, who has reached the last 16 in her last two appearances in Melbourne, is still seeking her first professional singles title.
She is not expected to face a serious challenge before that stage this year, when she is scheduled to face American 11th seed Chanda Rubin.
The eighth seed faces Hungarian Rita Kuti Kis in the second round.