Barty, who missed out on the chance of defending her title at Roland Garros last year due to coronavirus restrictions, struggled with a back issue but still prevailed 6-4 3-6 6-2.
The top seed had 18 winners to 25 unforced errors as she made it eight wins in Paris, where either Magda Linette or Chloe Paquet await in the next round.
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She had little trouble in seeing out the first set, hitting 80 per cent of her first serves, but she became passive from that point on and her opponent took advantage in the second set.
World number 70 Pera earned the only break in the second game and took her second set point to level up the contest.
Barty then had a scare as she called a medical time out at the beginning of the deciding set, but she looked a lot more focused from that point on.
The Australian saved the two break points she faced and broke Pera in the sixth and eighth games to pick up the victory in exactly two hours.
“This court is very close to my heart,” Barty said in her on-court interview. “It’s so nice to play here in front of fans, you make it enjoyable for players.
“Thank you very much. I just keep fighting. I was able to build more pressure in the third set which was important but Bernarda played an incredible match.”
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