Victory put him into a 13th Melbourne quarter-final to move fourth on the all-time list behind Roger Federer, Nadal and John Newcombe.
It is his 54th Grand Slam quarter-final in total -- second only to the retired Federer's 58.
De Minaur, who recorded his first victory against a top-five player in November when he beat Daniil Medvedev at the Paris Masters, was always facing an uphill climb.
Djokovic has not lost in Melbourne since 2018 -- he did not play in 2022 -- and has now won 25 consecutive matches at the Australian Open.
He always had the measure of the young Australian and broke to love in game six, consolidating without dropping a point for 5-2.
With de Minaur struggling under the pressure, he sent a baseline forehand long to hand the Serb another break and the set in just 35 minutes.
Only 54 percent of De Minaur's first serves went in compared to Djokovic's 76 percent, with the winners 9-1 in favour of the dominant Serb.
De Minaur won the sixth game in the second set, ending a run of nine consecutive losses, but it was only a brief moment of respite.
Djokovic stretched his hamstring at the changeover and immediately applied pressure again on De Minaur's first service game to break again in the third set, all but ending the match.