The world number one raced to a 6-2 6-3 6-4 triumph in less than two hours at a packed Rod Laver Arena, extending his winning streak against the Australian to 15 matches.
Federer made a slow start to the tournament but has been improving with every match.
He can expect a tougher test against Nikolay Davydenko after the Russian advanced with a 6-2 7-5 4-6 6-7 6-3 victory over Fernando Verdasco, but after hitting 49 winners against Hewitt he will go in with every confidence.
"Even though the scoreline (suggests) something else tonight, I had to really dig deep and come up with some amazing shots to beat him," Federer said.
"I was really able to press on the offensive, serve well when I had to, and I moved well as well. I'm very pleased with my performance tonight.
"When you can really produce them in the most important stages of a match it's so rewarding and such a good feeling that all the hard work you put in in the off-season is (worthwhile).
"It's just a beautiful feeling, you know."
He added: "I always knew it would be extremely hard. It was. I'm sweating bullets."
Hewitt has not beaten the Swiss since the 2003 Davis Cup semi-final when he came from two sets down to win in five.
The pair first played each other when they were 14 and just starting out on the junior circuit. They are both now 28, married with children, but the gulf between the current and former world number ones has never looked wider.
"It's always disappointing when you lose in a Grand Slam but he played special tennis," Hewitt said. "He hasn't played too many bad matches against me."
Hewitt retains the fighting spirit of old but injuries have taken their toll. As one of the smaller men in the game, he spends a lot of time behind the baseline trying to retrieve the ball as the bigger players pin him back.
He remains vulnerable on serve and had to struggle hard in most of games whereas Federer had no real problems apart from giving up a service break in the third set.
"I'm a great frontrunner," Federer said. "I feel like if he gets the first set, it's gonna be a really close match, whereas if I win the first set, it's always gonna be hard for him."
Sixth seed Davydenko's victory over ninth seed Verdasco was a five-set, tense affair.
The Russian, the form player on the men's tour over the past six months, had not lost a set coming into the match but the Spaniard showed in the third and fourth sets that he was vulnerable.
Verdasco, who made the Australian Open semi-finals last year, sent the match to a deciding set, however, the Russian achieved the crucial break in the sixth game and clinched victory when the Spaniard's return crashed into the net.
"(Federer is) number one, I'm number six," Davydenko said ahead of their clash. "Why (would I think) I need to be favourite if I'm not number one?
"He is always favourite for me. But on the court, I try to change my mind. I feel (if) I have then chance to win a set, and the next set, I realise (it)."
Former champion Novak Djokovic charged into the quarter-finals, thrashing Poland's Lukasz Kubot 6-1 6-2 7-5.
Kubot, who was given a walkover in the previous round after Russia's Mikhail Youzhny pulled out injured, was completely outclassed by Djokovic, who committed only 17 unforced errors in wrapping up the match in less than two hours.
The 86th-ranked Pole offered belated resistance in the third set, but Djokovic broke him at 5-5, then sealed victory on the second of three match points with an imperious forehand winner.
The third-ranked Serbian will meet Jo-Wilfried Tsonga, who he beat to win the 2008 title at Melbourne Park, for a semi-final place.
"Jo can beat anyone if he's really on the roll and if he starts hitting the ball well," Djokovic said.
"I just to have keep pressuring him and just apply my style of the game, not allow him to control the match. I'm happy with the way things are going. I won this tournament two years ago, so I just look forward to the upcoming challenges. I'm ready to give my 100 per cent and try to get a step further."
The 24-year-old Frenchman celebrated his first five-set match with a grinding win over Nicolas Almagro, winning 6-3 6-4 4-6 6-7(5) 9-7 in three and a half hours.
"It was good. Good to win in five sets, first time for me ... when you win your first five-set match, you're happy," the 10th-ranked Tsonga saod.
While Tsonga was happy for the win over 26th-seeded Almagro, a grizzled veteran by comparison with 11 five-set matches to his name, he could well have saved himself the effort.
After wrapping up the first two sets with a break in each, Tsonga threw away the third with a double-fault after conceding his first break point when trailing 5-4.
He then sprayed two unforced errors to concede a tiebreaker in the fourth to give Almagro hope of pulling off a famous theft.
The fifth proceeded as the fourth had done, both players slogging out long rallies but unable to break the other's serve, before Almagro was the first to blink when serving to stay in the match at 8-7.
Tsonga took a chance with a rush to the net and was rewarded with a match point, then smacked a forehand winner to seal it.
Since being defeated by world number three Djokovic in four sets for the 2008 title, the Frenchman has won four of their last five matches, but was beaten in straight sets in the last, a quarter-final at Miami last year.
His game plan would be to "stay aggressive, very aggressive, and give everything."
"What I learned (from the 2008 final), I don't know. But I beat him four times ... So I learned to beat him," he said.
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