Federer was barely detained by Krajinovic, the world number 41, as he moved smoothly through in 92 minutes in the night match on Rod Laver Arena.
Roger Federer says he will need an extra level of focus to cope with playing on the Australian Open courts if he is to go deep in Melbourne this year.
Top seeded Rafael Nadal will continue his 2020 Australian Open campaign with a second round match against Argentina's Federico Delbonis on Thursday, January 23.
The sixth game of the set proved pivotal, with Zidansek missing out on three break-point chances before just her fourth unforced error of the set gave Williams a game point that she finally converted, eliciting a shriek of "Come on!".
She will now face China's Qiang Wang.
"Each win is nice, because every single player in the main draw is unbelievable, is a player with a very high level", Thiem said.
In 2017, Djokovic was upset in the second round by Denis Istomin, who, like Ito, had earned his spot in the main draw by winning the Asia-Pacific wild-card playoff.
Having struggled through a four-set grind against unseeded German Jan-Lennard Struff in his opener, Djokovic was back to his imperious best as he fired down 16 aces and racked up 31 winners in a 95-minute romp at a gusty Rod Laver Arena.
Italy's Fabio Fognini, two sets down against America's Reilly Opelka when their match was suspended on Monday, returned to win it in five on Tuesday after a stormy encounter when both players argued furiously with the umpire.
"More so just to throw a spanner in the works for Roger".
"It's only the second round".
"I thought it wasn't 100% fair that he played three-and-a-half hours yesterday and me zero", Federer said in an on-court interview.
He scrambled to retrieve a drop-shot and flicked a cross-court forehand victor at full-stretch to bring up set point then converted it with an ace.
Although a finalist at the inaugural ATP Cup, Nadal will be less than happy with a loss to David Goffin and particularly a straight set loss to Novak Djokovic in the final tie, with Serbia prevailing as a result.
The Serb now faces Japan's Yoshihito Nishioka after he knocked out British number one Dan Evans in straight sets. "I made so many errors in a row and I just had to battle through that, through my own internal problems", the 23-time major victor said.