The top-seeded Australian won 6-4, 3-6, 6-2 and will next face either Magda Linette of Poland or French wildcard Chloe Paquet.
Barty skipped the defence of her title in 2020 due to the pandemic but has been in rich form this year.
The 25-year-old has won trophies at the Yarra Valley Classic, Miami and on clay in Stuttgart in the run-up to Roland Garros.
After easing through the first set on Court Philippe Chatrier on Tuesday, Barty went off the boil in the second and called for the trainer at the changeover.
The Australian had arrived on court with a heavy strapping on her leg having also suffered a tournament-ending abdomen injury in Rome two weeks ago.
However, she broke the 70th-ranked Pera for a 4-2 lead in the decider and never looked back.