The second seed had looked a little rusty in his opening win over Fabio Fognini, losing the first set, but today he was on form from the first shot.
Being under the roof on Centre Court certainly helped, and Djokovic wrapped up victory in 54 minutes to set up a last-16 clash with either Croatia's Marin Cilic or Lleyton Hewitt of Australia.
Rain frustrated those on the outside courts but Cyprus' Marcos Baghdatis beat the deluge to defeat French 16th seed Richard Gasquet 6-4 6-4.
The result meant a huge amount to Baghdatis, who will now meet third seed Andy Murray in a repeat of their late-night clash at the same stage of Wimbledon a month ago.
The 27-year-old said: 'It's great emotions. I want to thank whoever is up there for giving me this chance to be part of this life, and that's why I kissed the court.
'I am in the last 16 of an Olympic event and that's an incredible thing for me, and I hope I will keep going.'
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