Defending men’s champion Djokovic, winner of the event on five occasions, did notquite reach top gear but he still proved too strong for Italy’s Andreas Seppi.

The world number one, who yesterday denied allegations that he deliberately lost a match at the Paris Masters in 2007, branding them as “absurd”, took advantage of a catalogue of unforced errors from the Italian to progress to the next round by sealing a 6-1, 7-6, 7-5 success.

He will face Frenchman Gilles Simon in round four.

Williams, a six-time winner of the Australian Open, looked in superb form as she raced to a 6-1, 6-1 victory over 18-year-old Russia's Darya Kasatkina in just 45 minutes.

The American, who came into the event off the back of a withdrawal through injury at the Hopman Cup, will take on another Russian in the fourth round, world number 58 Margarita Gasparyan.

“Everything I've been trying to work on was kind of clicking today,” Williams said.

“My first match I thought I gave a great effort.

“My second match I thought, under the circumstances, I thought I played well.

“Hopefully with each match I can just do better.”

Elsewhere on another busy day in Melbourne, third seed and 17-time Grand Slam champion Roger Federer of Switzerland won his eagerly-anticipated battle with Bulgarian Grigor Dimitrov.

The Swiss maestro took the first set but dropped the second before he found his rhythm, emerging with a 6-4, 3-6, 6-1, 6-4 victory to earn his 300th Grand Slam win.

Home hope Nick Kyrgios, one of the game’s most controversial characters, suffered a 6-3, 6-4, 1-6, 6-4 defeat to Czech sixth seed Tomas Berdych in a match where his notorious temper flared up once more.

Kyrgios, who has already been in the headlines for the wrong reasons at the tournament after he was fined for uttering an audible obscenity during his first round victory against Spain's Pablo Carreno Busta, aimed a foul-mouth tirade at umpire James Keothavong in the third set, claiming he was being distracted by music being played in the stands.

In the women’s draw, Russian Maria Sharapova, who lifted the Australian Open crown in 2008, was made to work hard for her place in the last 16 as she progressed with a 6-1, 6-7, 6-0 win over unseeded American Lauren Davis.

It was the 600th victory of her career.

Australia’s Daria Gavrilova, conqueror of two-time Wimbledon champion Petra Kvitová of the Czech Republic in the second round, dumped another seed out of the tournament as she beat 28th seed Kristina Mladenovic of France 6-4, 4-6, 11-9 in a marathon contest.