World No 1 and top seed Djokovic reached the last-16 in Paris for the sixth straight year with a 6-4 6-4 6-4 win over 19-year-old Australian Kokkinakis.
Djokovic, bidding for a first Roland Garros title to complete a career Grand Slam, will face either South African 15th seed Kevin Anderson or French 20th seed Richard Gasquet for a place in the quarter-finals.
There was no sign of the hip problem which bothered him in his second round tie against Gilles Muller as he swept past his world No 84 opponent.
He fired 34 winners and didn’t face a single break point in his one-hour, 49-minute win over the highly-rated wildcard.
“Thanasi has a lot of talent and strength. He is still a teenager and he has plenty of time to do great things,” said Djokovic after winning his 25th successive match this season.
“I hope he does as he has a lot of qualities.”
Marin Cilic, the ninth-seeded US Open champion, continued his quiet progress to reach the fourth round for the third time.
The 26-year-old eased past Leonardo Mayer, the Argentine 23rd seed, 6-3 6-2 6-4 and will take on either 2013 runner-up David Ferrer or Simone Bolelli for a quarter-final slot.
Cilic has dropped serve just once in 40 games so far.