Switzerland's Roger Federer in action during the match against Serbia's Filip Krajinovic. Photograph:( Reuters )
Federer's next match is against John Millman.
Starting his second-round match at around 2100 local time on Rod Laver Arena, the six-time champion appeared to be in a hurry to finish the contest, breaking his opponent's serve twice in the first two sets and thrice in the third.
Krajinovic took a medical timeout to have his right upper arm attended with Federer leading 2-1 in the third set but it made no difference to the momentum for the 20-times Grand Slam champion, who hit his 42nd winner to end the contest in a little over 90 minutes.
He breezed through the next four games and hit a crosscourt forehand winner - his 42nd of the night - to end the contest in a little over 90 minutes.
Krajinovic's first outing against a top-five player at a Grand Slam ended up being a forgettable occasion.
The 41st-ranked player had his first-round match against Quentin Halys postponed due to rain on Monday and faced Federer after needing almost four hours to battle past the French qualifier in five sets on Tuesday.
"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. "The rain helped me. I do feel a little bit sorry actually like this but you have to take advantage of it."
Krajinovic's first serve percentage in the first two sets was almost 90%, which Federer called "rare". But it had no impact on the outcome of the match.
Unlike his main rivals, Federer, who won his last major title in 2018 at Melbourne Park, opted out of the inaugural ATP Cup in Australia to spend more time with his family before launching his 22nd season on Tour.
"I prefer this much more than (being) overcooked," Federer told reporters. "As easy as it looks, there's always the effort, trying to extend the lead.
"Of course, it's not quite the same stress level if you're down a set or a break or two sets, whatever it may be. I prefer it this way because you have always extra left in the tank if you need it."
"He's a super good guy, unbelievably tough opponent," Federer said. "There are not many fitter guys than him out there and those are the guys I respect the most, actually.
"He gets absolutely the most out of the game and I hope it is going to be a great match with some great rallies."