Djokovic, who won the last of his 12 majors at the 2016 French Open, is now fourth on the list Grand Slam winners – one behind Pete Sampras.
For Anderson, competing in his second major final, it was a day to forget.
Usually such a prolific server, the South African was broken four times in the opening two sets as Djokovic stormed into the lead.
Anderson, who has spent 11 hours on court this week, had treatment on his right bicep after the first set and seemed to grow into the match as it wore on.
The 6ft 8ins giant had five set points to take it into a fourth at 5-4 and 6-5 – only to squander them all.
Djokovic then moved up a gear in the tie-break to take a 6-2 6-2 7-6 win in 2hr 18mins.
The Serb’s win extended the domination of the big four – Roger Federer, Rafael Nadal, Andy Murray and himself. The quartet have now won 48 of the last 53 major championships.