0425 GMT January 19, 2019
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, AFP reported.
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 Swiss 19-time Grand Slam winner next plays little-known Hungarian Marton Fucsovics for a place in the quarterfinals.
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.
The Serb, who is on his way back after six months out with right elbow trouble, will next play South Korea's Chung Hyeon, who shocked fourth seed Alexander Zverev.
With the temperatures a manageable 26 Celsius (79 Farenheit) at Melbourne Park after two days of oven-like conditions, Zverev was beaten in five sets.
In a glamour evening tie, Sharapova was no match for Kerber, flopping 6-1, 6-3.
They 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 will face Taiwan's Hsieh Su-wei for a place in the quarterfinals.
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 grueling 3hr 44min epic that took its toll.
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.
In contrast, US Open finalist Madison Keys was in fine touch as she benefits from the guidance of former great Lindsay Davenport.
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.