The first player from an Asian country to win the U.S. Open singles title, Osaka was hampered by a back injury towards the end of last season and withdrew from the Sydney International in the leadup to Melbourne Park after making the Brisbane semi-finals.
Osaka called for the trainer and took medication when leading 2-1 in the second set against Zidansek but otherwise appeared in rude health as she bashed her way to a rousing 6-2 6-4 win.
"I was able to finish and win the match, so it's not that big of a deal," the Japanese 21-year-old told reporters.
"It's something that I have to keep an eye on. I'm not telling you, though.
"You'll never guess. You'll never find out," she added with a smile.
Fourth seed Osaka reached the fourth round of last year's Australian Open and has been getting used to the attention that comes with being a Grand Slam champion after New York.
She said she still felt too new to the tour to feel comfortable hugging her rivals after matches and preferred a handshake-first policy.
"The thing is, I'm used to handshakes. Every time someone comes for a hug, I'm very confused," she said.
"I'm told that I give out the worst hugs, too.
"It's not necessarily the best situation for me to try to hug someone unless I really know them. And I don't really know anybody, so."
Osaka, who will play Taiwan's Hsieh Su-wei for a place in the fourth round, gave a second serving of joy to Japanese fans, who had watched compatriot Kei Nishikori close out a five-set cliffhanger against Ivo Karlovic on the previous match at Margaret Court Arena.
Osaka ran into Nishikori, Asia's first male Grand Slam finalist when he made the 2014 U.S. Open title-decider, when walking in the tunnel through to the court before her match.
"I told him, 'Nice match'. He looked very tired. I was just like, 'Oh, excuse me, I'll get out of your way. You had a very, very long match. I had to warm up four times, so thank you for that.'"
(Editing by Amlan Chakraborty)
