There was a moment of relief for the Hungarian when she finally found her way onto the scoreboard in the sixth game, having to save a set point to do so.
But that was barely a speed bump in Williams' race through the match.
It was the former world No.1's third comfortable straight sets win of the tournament, but she still described her form as "rusty".
"I am nowhere near where I want to be," Williams said.
"I was a little rusty. I'm just trying to play through the rust."
But Williams, who has claimed the title on five of her past seven trips to Melbourne Park, already looks to be finding the kind of form to have her looming large as a contender this year, particularly given her seemingly unrestricted physical condition.
Williams will next meet unseeded Russian Ekaterina Makarova, before a potential quarter-final clash with 2008 Open winner Maria Sharapova.
Sharapova has also been in excellent touch, dropping a total of five games in the first three rounds.
- AAP