The world number one from Serbia showed no ill-effects from a groin problem he suffered during his previous match, ending the tennis lesson on his first match point when teenager Kokkinakis returned a first serve wide.
Kokkinakis had moments of brilliance on court Philippe Chatrier, sometimes bothering Djokovic with his booming forehand, but he never got into his opponent's serve.
Djokovic, who did not face a single break point, will next face either local favourite Richard Gasquet, the 20th seed, or South African 15th seed Kevin Anderson.
Djokovic looked in fine form after skipping practice.
"I haven't hit the ball yesterday and just had an agreement with the team that it's better for me to skip the tennis practice," he told a news conference.
"I have had enough tennis in the last couple of months. It wasn't enough of my concern if I'm going to keep in shape or not if I don't play a day. Body feels fine today, absolutely recovered from the last match, and that's it."
Djokovic did not have to do much for his only break in the first set, hitting a single winner in the fifth game.
That was followed by two errors from his teenage opponent and a deep ball foxed him by skipping high off the baseline.
The break came earlier in the second, but it was far from one-way traffic.
Kokkinakis looked comfortable in the long rallies, hit some exquisite drop shots, and thrilled the Paris crowd to shouts of "allez Kokki " by battling back from 0-40 down to hold serve and go 2-1 ahead in the third.
But Djokovic broke decisively in the fifth game when he benefited from one of Kokkinakis's numerous unforced errors.
"It just shows kind of where I need to get to. I don't think I need to change too much what I'm doing," Kokkinakis said.
"I think I'm on a good path. I'm not happy that I didn't return great, I don't think. But he was hitting his spots really well on his serve and it made it tough for me. That was probably the one thing I was disappointed with today."
Djokovic, who is on a 25-match winning streak, has a potential quarter-final meeting with nine-times champion Rafa Nadal of Spain.
(Reporting by Julien Pretot; Editing by Ed Osmond)
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