BBC SPORT | Tennis | Measured Federer beats Baghdatis
The Swiss star played within himself but it was still enough to beat qualifier Marcos Baghdatis of Cyprus.
Federer was broken after racing into a 3-0 lead, but it was the only setback he suffered in a measured display.
The charismatic Baghdatis battled manfully in the third set and played some extravagant shots before going down in a tie-break 6-2 6-2 7-6 (7/4).
"I enjoyed the battle," said the 23-year-old Federer.
"He didn't play great in the first two sets but then he stepped it up and after you've won it's good to have battled it out.
"I'm very happy. I've saved a lot of energy. It's like the tournament almost starts now for me, which is very good.
"I'm looking forward to tough matches coming up now but I'll try to look at the big picture and defend my title.
The world number one now faces a quarter-final against four-time Australian Open winner Andre Agassi.
"I think I've proven myself in the past, and I know my game's good enough," he added.
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Roger offers me the opportunity to push myself more than I've been pushed in a long time
"Even on my day when I'm not playing perfect, I know I can beat him. He's not as good as he was when he was at the top of the ranking, otherwise he would be there. Fortunately, I'm there.
"I think he has to raise his game, not me."
Fourth seed Marat Safin overcame the stubborn challenge of Belgian Olivier Rochus to reach the quarter-finals.
Safin recovered from dropping the first set to beat Rochus 4-6 7-6 7-6 7-6.
The Russian, twice a runner-up at Melbourne Park, received a warning in the fifth game of the third set.
Having missed three chances to break, he smashed his racket and was given a warning by the umpire before recovering his composure for victory.
He will next face Slovakia's Dominic Hrbaty who claimed a 7-5 6-3 6-1 win over Thomas Johansson of Sweden.
Johannson, the 2002 champion down under and 30th seed, had needed five sets to win each of his opening three matches and had nothing left in the tank against the 20th seed.
After a tight first set it was one-way traffic as Hrbaty sealed the win in one hour 41 minutes.
"I got through quickly and I can save energy for my next match," he said.