The two greats of the game -- who have won 11 Australian Opens between them -- could meet in the last four if they maintain their winning ways.
Defending champion Federer was never troubled by France's Richard Gasquet, who has failed to take a set off him since 2011, as he steamed into the last 16 with a 6-2, 7-5, 6-4 win.
"The second set was tight, the match was close and I had to focus to the very end," said the Swiss 19-time Grand Slam winner, who next plays little-known Hungarian Marton Fucsovics for a place in the quarter-finals.
Djokovic was equally convincing in his 6-2, 6-3, 6-3 rout of Spanish 21st seed Albert Ramos-Vinolas, although there was concern when he sought a medical timeout for treatment to his lower back.
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"It was straight sets but I had to earn my points," insisted the Serb, who is on his way back after six months out with right elbow trouble.
"Obviously for me it's taking it one match at a time but I have to be more humble with my expectations as I haven't played in the last six months."
He next plays South Korea's Chung Hyeon, who shocked fourth seed Alexander Zverev.
He has been hailed as the leader of the tennis new guard but has now failed to go beyond the fourth round in 11 Grand Slams, admitting he has "some figuring out to do".
In a glamour evening tie, Sharapova was no match for Kerber, flopping 6-1, 6-3.
They pair are both 30, former world number ones and were the only two Australian Open winners left in the women's draw, but there was only one player in it.
Kerber is in scintillating form, having won the lead-up Sydney International, and will face Taiwan's Hsieh Su-wei for a place in the quarter-finals.
For Sharapova, who is looking to rediscover her best on her way back from a 15-month drugs ban, it is back to the drawing board.
"I think there are a lot of things that I need to get better at and improve on," she admitted.
- Took its toll-
World number one Simona Halep is lucky to be still in contention after surviving three match points in a titanic struggle against 76th-ranked American Lauren Davis.
She looked out for the count at one point but finally got over the line 4-6, 6-4, 15-13 in a gruelling 3hr 44min epic that took its toll.
"I'm almost dead," the tenacious Romanian said after the incredible battle, in which Davis lost a toenail and Halep served for the match four times.
The former quarter-finalist will now play Naomi Osaka after the Japanese star beat Australia's Ashleigh Barty.
Sixth seed Karolina Pliskova also had a tough test, beating fellow Czech Lucie Safarova 7-6 (8/6), 7-5.
Flying under the radar, the 17th seed has surrendered just 16 games on her way to the fourth round after beating Romania's Ana Bogdan 6-3, 6-4.
She will next face French eighth seed Caroline Garcia, who was too strong for Belarussian Alaksandra Sasnovich.
Among the men through was Austrian fifth seed Dominic Thiem and veteran Tomas Berdych, along with American Tennys Sandgren, who had never won a Grand Slam match before this year's Australian Open.