The Serbian, who has burst back to form this year, winning Wimbledon and the US Open, broke the Frenchman in the fifth game on the way to a 6-3 7-5 victory to ease into round three.
The 31-year-old Djokovic had to contend with a more stubborn Chardy in the second set, before the second seed's superior shot-making won through in 83 minutes.
The 14-time Grand Slam champion missed six months of competition in 2017 and had elbow surgery at the start of this year.
But he has surged back to form and fitness and now has his eye on Rafael Nadal's number one ranking.
Top seed and holder Federer starts his campaign on Wednesday against Russia's Daniil Medvedev.
The 26-year-old Basilashvili will now have another upset in his sights when he plays fourth seed Alexander Zverev at the Masters 1000 event on Wednesday. Basilashvili's victory over an under-the-weather del Potro at the weekend was just his second ATP title, the first coming in Hamburg in July.
A press conference for the Argentine on Tuesday was cancelled at the last moment, however, which suggests that he could still be unwell.
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