Djokovic passes Tiafoe test, Serena sublime at Australian Open
Women's favourite Naomi Osaka also charged through but fellow major winners Stan Wawrinka, Bianca Andreescu and Petra Kvitova were all second-round casualties.
Among the late matches, Aussie crowd-pleaser Nick Kyrgios served underarm, smashed a racquet and rowed with the chair umpire before coming from behind to beat France's Ugo Humbert in five gripping sets.
Earlier, Djokovic was given a stern examination by American Frances Tiafoe and dropped his first set of the tournament before recovering to win 6-3, 6-7 (3/7), 7-6 (7/2), 6-3.
"I was fortunate to get through the third set today, it was anybody's game," said the defending champion, after his win in hot conditions in Rod Laver Arena.
The top seed looked in control after taking the first set, but lightning-quick Tiafoe, who reached the quarter-finals two years ago, refused to go away.
The American bounced back to take a close second set but imploded as tensions rose in the fourth, receiving a code violation for an audible obscenity as Djokovic took charge.
The Serb is targeting a record-extending ninth title and his 18th Grand Slam trophy overall as he snaps at the heels of Rafael Nadal and Roger Federer, who top the all-time list with 20 each.
He avoided the fate of 2014 winner Wawrinka, who blew three match points in the fifth-set tiebreaker in his four-hour epic with Marton Fucsovics, who won 7-5, 6-1, 4-6, 2-6, 7-6 (11/9).
"I hesitated a little bit when I had the match point and I lost it," said the 35-year-old Swiss, a three-time Grand Slam winner.
Osaka, whose three Grand Slam titles include the 2019 Australian crown, had no such trouble in her evening match against France's Caroline Garcia -- despite fearing defeat after a bad dream.
"Last night I had a dream that I lost this match, and I really didn't feel good about it," she said after the 6-2, 6-3 win.
Williams, 39, continued her quest to equal Margaret Court's all-time mark of 24 Grand Slams with a 6-3, 6-0 romp past 99th-ranked Serbian Nina Stojanovic.
"I'm here to have fun and it's great to be playing in front of a crowd," said Williams.
With Australia virtually virus-free, the tournament is welcoming the biggest Grand Slam crowds since the pandemic, although attendances are well down on previous years.
A socially distanced John Cain Arena was rocking for the Kyrgios match, where the unseeded home favourite denied Humbert what seemed like a certain win to set up a clash with US Open champion Dominic Thiem.
"Honestly, I don't know how I did that," said Kyrgios after the unlikely 5-7, 6-4, 3-6, 7-6 (7/2), 6-4 victory.
"I don't even know what to say, I'm lost for words. That is one of the craziest matches I've ever played."
German sixth seed Alexander Zverev went through in less compelling fashion, grinding past America's Maxime Cressy 7-5, 6-4, 6-3.
Williams' elder sister Venus, 40, was among the casualties on day three when she painfully rolled her ankle in the first set against Sara Errani before hobbling through a 6-1, 6-0 defeat.
And Andreescu, the 2019 US Open champion who missed the entire 2020 season with a knee injury, saw her comeback come to an abrupt end 6-3, 6-2 against Taiwan's Hsieh Su-wei.
Elsewhere Kvitova, the former Wimbledon champion and Melbourne runner-up in 2019, committed 44 unforced errors in her 6-4, 1-6, 6-1 defeat to Romania's Sorana Cirstea as the big names tumbled on day three.
However Thiem, runner-up to Djokovic last year, was all smiles as he beat Germany's Dominik Koepfer 6-4, 6-0, 6-2.
"It was great, to be honest," said the Austrian of his performance.
Eighth seed Diego Schwartzmann of Argentina beat France's Alexandre Muller 6-2, 6-0, 6-3, while Canada's Milos Raonic won 6-7 (1/7), 6-1, 6-1, 6-4 against another Frenchman, Corentin Moutet.