Djokovic was alway going to be favoured in this contest but he had never met the Frenchman before, as such uncertainty reigned.
The former World No 1 commended Lestienne's game as he savoured the 6-3 6-2 victory in Adelaide.
"For the first match I can't complain," said the 21-time grand slam winner.
"I played very well. I thought the first six games were very competitive and I have never faced him before. He is a counterpuncher, he doesn't make too many mistakes. He has a tricky serve, hits his spots. But once I made that break at 3-2 in the first set I thought I stepped it up and played really good tennis for the rest of the match."
Djokovic steadily worked his way up towards firing on all cylinders during a deliberately executed straight sets victory.
The nine-time Australian Open is looking to extend his record number of wins at the Grand Slam later this month.
The Serbian goes on to face another Frenchman in Quentin Halys who battled beyond Australian wildcard Jordan Thompson to gain the last 16 and a huge match-up with a playing legend.
Meanwhile third seeded Daniil Medvedev appeared on course for a tight and tense battle with Lorenzo Sonego before injury struck the Italian early in the second set.
Medvedev had edged Sonego out in the first set tiebreaker and led 2-1 when the Italian was forced to quit.
The Russian had faced nine break points on his way to claiming the first set, in what he described as a crazy match.
"It was crazy. It's probably the first time I've saved nine set points in my life," said Medvedev, who was leading 7-6(6), 2-1 when the match ended.
"What a match to start the year! It was unfortunate for everyone that it had to finish early and I wish Lorenzo a speedy recovery."
"It was a great match and I was actually surprised that Lorenzo retired. Great match. I think the level could be better from both of us at some moments, but considering that it's the first match of the year I feel like it was a great fight."
The Round of 16 holds a meeting with Serbian No 2 Miomir Kecmanovic who forced his way beyond Aussie wildcard Christopher O'Connell in straight sets.