
Tsitsipas, the first Greek to lift an ATP trophy when he beat Ernests Gulbis in Stockholm on Sunday, earned his 40th victory of the season by seeing off long-time training partner Chardy.
“It was a good win for me today, I’m happy with my performance,” said Tsitsipas, the world number 16.
“It was tough to come back after winning a title last week. But I’m excited about what’s to come in my tennis.”
Tsitsipas took revenge over Chardy for a loss to the Frenchman in Montpellier in February.
The 20-year-old had accumulated only four career tour-level match victories coming into 2018, but has enjoyed a breakthrough season and will take on Germany’s Peter Gojowczyk next in Basel.
Second seed Alexander Zverev notched his tour-leading 50th win of the season as he brushed past Dutchman Robin Haase 6-4, 7-5 in his debut at the event.
The German, who has secured a spot in the ATP Finals in London next month, managed to overcome 19 unforced errors in the opening set.
He lost serve while trying to close out the match, but recovered to advance.
Zverev will face Australian qualifier Alexei Popyrin in round two.
However, 2016 champion and third seed Marin Čilić crashed out 7-5, 7-6 (7/2) to Romania’s Marius Copil in his second-round match.
Taylor Fritz beat Swiss wild card Henri Laaksonen 6-2, 7-5 and will meet Copil in the last eight.
Latvia’s Gulbis received on-court treatment around his hip muscle area on the way to a 7-5, 6-4 victory over fifth seed Jack Sock.
The defeat dropped the American’s record this year to a dreadful 7-20 as he lost for the sixth time in his last seven matches.
Spanish eighth seed Roberto Bautista Agut defeated Portugal’s João Sousa 6-4, 6-3, while Serbian Dušan Lajović beat Adrian Mannarino of France 6-7 (4/7), 6-1, 6-2.