No. 2 men's seed Djokovic prevailed 6-3, 6-2, 6-2 over Japan's Yoshihito Nishioka in 85 minutes.
Williams, meanwhile, was ousted by Wang Qiang in a tight three-setter.
Serena was not the only big name knocked out on Friday. Defending women's champion Naomi Osaka became 15-year-old Coco Gauff's latest victim, and men's No. 6 seed Stefanos Tsitsipas lost to Milos Raonic.
Roger Federer survived a huge scare against John Millman, eventually coming through 6-4, 6-7 (2), 4-6, 6-4, 7-6 (8) against the Australian.
Elsewhere, top women's seed Ashleigh Barty advanced after beating Elena Rybakina 6-3, 6-2, and former world No. 1 Caroline Wozniacki called time on her career after losing to Tunisia's Ons Jabeur.
Here are some key results from Friday's action. For the complete results, visit the Australian Open's official website.
(2) Novak Djokovic bt. Yoshihito Nishioka: 6-3, 6-2, 6-2
(14) Diego Schwartzman bt. (24) Dusan Lajovic: 6-2, 6-3, 7-6 (7)
Marton Fucsovics bt. Tommy Paul: 6-1, 6-1, 6-4
Marin Cilic bt. (9) Roberto Bautista Agut: 6-7 (3), 6-4, 6-0, 5-7, 6-3
Tennys Sandgren bt. Sam Querrey: 6-4, 6-4, 6-4
(32) Milos Raonic bt. (6) Stefanos Tsitsipas: 7-5, 6-4, 7-6 (2)
(3) Roger Federer bt. John Millman: 6-4, 6-7 (2), 4-6, 6-4, 7-6 (8)
(12) Fabio Fognini bt. (22) Guido Pella: 7-6 (0), 6-2, 6-3
(1) Ashleigh Barty bt. (29) Elena Rybakina: 6-3, 6-2
(27) Wang Qiang bt. (8) Serena Williams: 6-4, 6-7 (2), 7-5
(7) Petra Kvitova bt. (25) Ekaterina Alexandrova: 6-1, 6-2
(22) Maria Sakkari bt. (10) Madison Keys: 6-4, 6-4
Ons Jabeur bt. Caroline Wozniacki: 7-5, 3-6, 7-5
(8) Alison Riske bt. Julia Goerges: 1-6, 7-6 (4), 6-2
Coco Gauff bt. (3) Naomi Osaka: 6-3, 6-4
(14) Sofia Kenin bt. Zhang Shuai: 7-5, 7-6 (7)
Djokovic was ruthless in his dismantling of Nishioka. His serving was superb, with 74 per cent of his first serves finding their mark and 17 of his points coming via aces:
The Serbian offered up just one break point, which he saved, while winning five of the six break points he earned when Nishioka had the ball in hand, and he hit 40 winners to his opponent's 15.
Djokovic will now meet No. 14 seed Diego Schwartzman, who he has beaten on all three previous occasions they have met.
Raonic and Tsitsipas had never met before Friday, but the Greek 21-year-old was a strong favourite against the injury-plagued Canadian.
Unfortunately for Tsitsipas, though, he came up against Raonic showing the type of form that got him to No. 3 in the world in 2016.
The 29-year-old prevailed in two-and-a-half hours, hitting 19 aces and 55 winners.
So clinical was Raonic's serving that he did not offer up a single break point in the entire match:
Serena bemoaned her poor performance after her shock loss against Wang:
The American icon was some way from her imperious best, and the immaculate Wang found herself serving for the match at 5-4 in the second set.
Like so many before her, the Chinese No. 27 seed blinked, and Williams levelled the match up by winning the subsequent tiebreak.
It seemed inevitable the seven-time Melbourne Park champion would then go on to win.
But Wang continued to cause Serena problems and eventually claimed a well-deserved victory with her third match point.
Williams' stats from the two hour, 41 minute contest paint a picture of the 38-year-old's struggles.
Her first serve was only at 56 percent, and she made a whopping 56 unforced errors compared to Wang's 20.
Jabeur is next in line for the 28-year-old after victory over Wozniacki:
The Dane, who won her sole Grand Slam at the Australian Open back in 2018, announced in December that 2020's opening Grand Slam would be her final tournament, and there were emotional scenes on the Melbourne Arena after her defeat:
Barty's campaign to win her home Grand Slam for the first time continued as she dispatched 20-year-old Rybakina in 78 minutes.
The world No. 1 claimed five breaks across the two sets and hit 28 winners. She will play America's Alison Riske in the next round.
Gauff's triumph was another impressive display of the teenager's cool temperament, but in truth, she did not have to work that hard for victory because Osaka was largely woeful, particularly in the second set:
At a set and a break down early in the second, the world No. 4 showed a glimpse of fight by breaking back with some big hitting.
But it did not prompt a comeback as she could not maintain her level, and all Gauff had to do was keep the ball in play long enough for Osaka to make a mistake, which she did with alarming regularity.