Svitolina, a three-time quarter-finalist in Paris, needed just 74 minutes to wrap up her win over Li, who was up a break in the second set but couldn't hold off her experienced opponent.
"It was a great start for me," Svitolina said. "In the second set I was 1-4 down, so it was really challenging. I was sweating a lot to get back into it and I'm very happy I won in straight sets in the end."
She next faces an in-form Barbora Krejcikova, who eased past No.32 seed Ekaterina Alexandrova 6-2, 6-3 to extend her current winning streak to seven matches in a row, having picked up the Strasbourg title last Saturday.
Ons gets her revenge
Tunisian No.25 seed Ons Jabeur had declared before her second round against Astra Sharma that she was "going for revenge" having lost to the Australian in the Charleston final less than two months ago.
Jabeur did just that as she eased to a 6-2, 6-4 victory over the world No.124.
The entertaining North African fired 24 winners against 18 unforced errors en route to a third-round meeting with Poland's Magda Linette.
Matteo in a hurry
Italian No.9 seed Matteo Berrettini booked his place in the third round in Paris for the third time in four years with a swift 6-3, 6-3, 6-2 result against Argentinean Federico Coria.
Berrettini, who had a standout clay-court season so far, winning the title in Belgrade and reaching the final in Madrid, awaits the winner of the second round between Kwon Soonwoo and Andreas Seppi.