Swiatek advances to face in-form Ukrainian Marta Kostyuk, who is unbeaten in 14 matches on clay this season following titles in Madrid and Rouen.
Third seed Swiatek dug herself out of an early 2-0 hole against her 35th-ranked opponent, who won their most recent meeting at Miami in March.
Swiatek broke three times in the opening set to nose ahead, and then surged into a 4-1 lead in the second set.
She overcame a stumble as she tried to close it out, before wrapping up victory in one hour and 25 minutes on another hot day at Roland Garros.
"It was a good match. I played much better than Miami," said Swiatek, who moved to appoint Francisco Roig, a longtime coach of Rafael Nadal, in the wake of her loss to Linette two months ago.
Kostyuk, the 15th seed, continued her fine run earlier with a 6-4, 6-3 win over Switzerland's Viktorija Golubic.
She is unbeaten in 15 matches on clay this season following titles in Madrid and Rouen.
"Marta is having a great season. She always had a game to play well," said Swiatek.
"So good for her. But I'm going to focus on myself, prepare tactically, as before any other match, and we'll see."